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710 |
Bounded analytic functions
- Garnett
- 1981
(Show Context)
Citation Context ...th constant or analytic coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], [15], [30], [33], =-=[34]-=-, [40], [49], [51], [52]. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundary value problems f... |

493 | The serial cultivation of human diploid cell strains. Exp Cell Res 25:585, - Hayflick, PS - 1961 |

277 |
Singular integral equations
- Muskhelishvili
- 1953
(Show Context)
Citation Context ... our aim Gotfried Wilhelm von Leibniz The theory of complex boundary value problems originating from the work of B.Riemann [35] and D.Hilbert [31] and developed by F.D.Gakhov [28], I.N.Muskhelishvili =-=[33]-=-, I.N.Vekua [42], W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equations of arbitrary order is explored after the basic fundamental solutions we... |

192 | The moulding of senescence by natural selection. - Hamilton - 1966 |

181 |
On a theorem of functional analysis
- Sobolev
- 1938
(Show Context)
Citation Context ...rary function of the class D01(G), f is said to be the generalized (weak) derivative of g with respect to z (to z). This definition is a particular case of the general one, which can be found in e.g. =-=[38]-=-. We take the definition of the Sobolev space as Definition 1.0.3. [38] The linear manifold of all summable functions ϕ(x1, x2, ..., xn) having on a finite domain D all generalized derivatives of orde... |

167 |
Boundary Value Problems
- Gakhov
- 1966
(Show Context)
Citation Context ...ons with constant or analytic coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], [15], [30], =-=[33]-=-, [34], [40], [49], [51], [52]. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundary value prob... |

144 |
Generalized Analytic Functions
- Vekua
- 1962
(Show Context)
Citation Context ...d Wilhelm von Leibniz The theory of complex boundary value problems originating from the work of B.Riemann [35] and D.Hilbert [31] and developed by F.D.Gakhov [28], I.N.Muskhelishvili [33], I.N.Vekua =-=[42]-=-, W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equations of arbitrary order is explored after the basic fundamental solutions were approached [1... |

112 | Metabolic stability and epigenesis in randomly constructed genetic nets. - SA - 1969 |

110 |
On the existence of certain singular integrals
- Calderón, Zygmund
- 1952
(Show Context)
Citation Context ...esses weak derivatives with respect to z and z, moreover ∂zTf = f, ∂zTf =: Πf, where Π is a singular integral being understood in the principle value sense. Integrals of such type are investigated in =-=[27]-=-. From the Cauchy-Pompeiu representation formula it follows that any function w ∈ C1(D;C) ∩ C(D;C) can be found by known values on the boundary and values of a first order derivative inside of the dom... |

100 |
The Equations of Mathematical Physics
- Vladimirov
- 1976
(Show Context)
Citation Context ...d for these equations. 3.5.1 Dirichlet, Neumann and Robin problems for the Poisson equation The Dirichlet and Neumann problems for the Poisson equation are wellknown in the literature, see e.g. [36], =-=[50]-=-. Here explicit solutions for these problems are specified for a ring domain. A Robin problem for the Poisson equation is posed and its solution is found in explicit form. Theorem 3.5.7. The Dirichlet... |

83 |
Complex Analysis
- Stein, Shakarchi
- 2003
(Show Context)
Citation Context ... i √ 3n)(3m− i √ 3n) = 9m2 + 3n2 ≥ 3(m2 + n2) m2 + n2 ≥ 2mn, m2 + n2 ≥ 1 2 (|m|+ |n|)2, |ωmn|3 ≥ (|m|+ |n|)3, therefore |ωmn| ≥ √ 3 2 (|m|+ |n|) > |m|+ |n|, 1|ωmn|3 ≤ 1 (|m|+ |n|)3 and by Lemma 1.5. (=-=[39]-=-, p.268) the series ∑ (n,m)6=(0,0) 1 (|m|+|n|)r , r > 2 is convergent, therefore the sum (5.7) is convergent. By the properties 10 − 30 the Green function G1(z, ζ) is uniquely defined. Obviously, G1(z... |

83 | Sir2 links chromatin silencing, metabolism, and aging. - GUARENTE - 2000 |

80 |
Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen
- Hilbert
- 1906
(Show Context)
Citation Context ...and even prove, that following that method we shall attain our aim Gotfried Wilhelm von Leibniz The theory of complex boundary value problems originating from the work of B.Riemann [35] and D.Hilbert =-=[31]-=- and developed by F.D.Gakhov [28], I.N.Muskhelishvili [33], I.N.Vekua [42], W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equations of arbitrary ... |

72 |
Elements of the Theory of Elliptic Functions
- Akhiezer
- 1990
(Show Context)
Citation Context ...ling with analytic functions. There are just few results known on this subject. Among them is the celebrated Villat's formula for the solution of Schwarz problem in a concentric ring domain, see e.g. =-=[3]-=-, [39], expressed in terms of Weierstrass ζ -function; and the formulas obtained by V.V. Mityushev and S.V. Rogosin [39] as well for the Schwarz and the Riemann-Hilbert problems as for the Riemann pro... |

66 | An Introduction to Classical Complex Analysis, - Burckel - 1979 |

31 |
Conformal and Potential Analysis in Hele-Shaw Cells,
- Gustafsson, Vasil’ev
- 2006
(Show Context)
Citation Context ...dition. 7 Concerning with applications, the case of multiply connected domains represents a special interest as it appears naturally in many problems of mechanics, especially in the filtration theory =-=[35]-=-, [42][44], in hydrodynamics, in the theory of composite materials [2], [39], etc. 8 Acknowledgements It is time to express my gratitude to those people who helped and supported me in writing this th... |

29 |
Complex analytic methods for partial differential equations. An introductory text
- Begehr
- 1994
(Show Context)
Citation Context ...re constructed and the solutions to the Dirichlet and the Neumann problems for the Poisson equation are presented. 3.1.1 Harmonic Green function and the Green Representation formula Definition 3.1.1. =-=[6]-=- A real-valued function G(z, z0) in a domain D of C having the properties: 1. G(z, z0) is harmonic in z ∈ D\{z0}, 2. log |z − z0|+G(z, z0) is harmonic in the neighborhood of z0, 3. limz→∂D G(z, z0) = ... |

29 |
Hele-Shaw flows with time dependent free boundaries involving multiply connected fluid region, Euro
- Richardson
(Show Context)
Citation Context .... 7 Concerning with applications, the case of multiply connected domains represents a special interest as it appears naturally in many problems of mechanics, especially in the filtration theory [35], =-=[42]-=-[44], in hydrodynamics, in the theory of composite materials [2], [39], etc. 8 Acknowledgements It is time to express my gratitude to those people who helped and supported me in writing this thesis. ... |

25 | Gustafsson L, Rigoulet M, Nyström T (2003) Asymmetric inheritance of oxidatively damaged proteins during cytokinesis - Aguilaniu |

16 | Boundary Value Problems for Analytic Functions - Lu - 1993 |

14 | Repair and its Evolution: Survival versus Reproduction, Chapter 7. Physiological Ecology: An Evolutionary Approach to Resource Use, Blackwell Scientific - Kirkwood - 1981 |

13 | 2003)Longevity regulation in Saccharomyces cerevisiae: linking metabolism, genome stability - KJ, Medvedik, et al. |

12 |
Conformal mappings and boundary value problems,
- Wen
- 1992
(Show Context)
Citation Context ...lytic coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], [15], [30], [33], [34], [40], [49], =-=[51]-=-, [52]. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundary value problems for multiply connec... |

12 |
Boundary Value Problems for Elliptic Equations and Systems,
- Wen, Begehr
- 1990
(Show Context)
Citation Context ...coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], [15], [30], [33], [34], [40], [49], [51], =-=[52]-=-. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundary value problems for multiply connected do... |

11 | Understanding the odd science of aging. Cell 120: 437–447 Kirkwood TBL (1977) Evolution of ageing. Nature 270, 301–304 Kirkwood TBL - TB - 2005 |

10 | Complex Variables - Berenstein, Gay - 1991 |

9 |
Zur Integration der partiellen Differential-Gleichung ∂2u ∂x2+ ∂2u ∂y2
- Schwarz
(Show Context)
Citation Context ...| < 1}. The kernel [5] ζ + z ζ − z , z ∈ D, ζ ∈ ∂D is called the Schwarz kernel and its real part ζ ζ − z + ζ ζ − z − 1 5 is the Poisson kernel for the unit disc with a property proved by H.A.Schwarz =-=[37]-=- lim |z|→1,|z|<1 1 2pii ∫ |ζ|=1 γ(ζ) ( ζ ζ − z + ζ ζ − z − 1 ) dζ ζ = γ(ζ), ζ ∈ ∂D (1.14) for γ ∈ C(∂D;R). The Poisson kernel for the upper half plane H = {z : Im z > 0} studied in [29] and it is 1 t−... |

9 |
Peetre: A Green's function for the annulus
- Englis, J
- 1996
(Show Context)
Citation Context ...r a circular ring domain leading to the solution of the respective Dirichlet problem for the biharmonic equation. The obtained biharmonic Green function differs from the Green function constructed in =-=[31]-=- for the bi-Laplace operator with a particular Dirichlet boundary condition. 7 Concerning with applications, the case of multiply connected domains represents a special interest as it appears naturall... |

7 | Boundary value problem in complex analysis,
- Begehr
- 2005
(Show Context)
Citation Context ...∂z, the Laplace operator ∂z∂z and the Bitsadze operator ∂ 2 z . The basic boundary value problems for complex partial differential equations have been considered for different particular domains, see =-=[2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 29, 32, 34, 41, 43, 44]-=-. They are explicitly solved as well for the inhomogeneous Cauchy-Riemann equation as for the Poisson equation. Among these particular domains the case of the unit disc is mostly considered and explai... |

7 | Evidence for the involvement of a cytoplasmic factor in the aging of the yeast Saccharomyces cerevisiae. J Bacteriol 171 - NK, SH - 1989 |

6 |
Boundary value problems for the inhomogeneous polyanalytic equations
- Begehr, Kumar
(Show Context)
Citation Context ...of powers of the Laplace operator, (∂z∂z) k, k ≥ 2. Different types of boundary conditions are prescribed for these equations. Some boundary value problems for the polyanalytic equation are solved in =-=[20]-=-, [8] in the case of the unit disk. To treat boundary value problems to the polyharmonic equation the concept of polyharmonic Green functions is developed. They are certain fundamental solutions for t... |

6 | Iterated Neumann problem for higher order Poisson equation. - Begehr, Vanegas - 2003 |

6 |
Basic complex boundary value problems in the upper half plane
- Gaertner
- 2006
(Show Context)
Citation Context ... for simply to multiply connected domains. The present thesis contributes to the research subject initiated by Prof. Dr. H. Begehr and developed by his students and collaborates [1], [5] [21], [29], =-=[32]-=-, [37], [47], [48]. A systematic investigation of boundary value problems for complex partial differential equations of arbitrary order on the base of integral representation formulas was initiated by... |

5 |
Z.X.Zhang, Polyharmonic Dirichlet problems
- Begehr
(Show Context)
Citation Context ...s. These are also potential operators. Other potential operators of this kind for higher order model operators are developed for certain simple domains and the boundary value problems are solved, see =-=[10, 11, 23, 24]-=-. In the present thesis the Cauchy-Riemann equation ∂zw = f and the Poisson equation ∂z∂zw = f in two particular domains are studied, namely a quarter ring and a half hexagon. The boundary of the quar... |

5 | A Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half
- Begehr, Gaertner
(Show Context)
Citation Context ...d Green function (the denotation was introduced by H. Begehr) [11], [12]. The results concerning boundary value problems for the polyharmonic equation are given in [22],[23] for the unit disk, and in =-=[14]-=- for the upper half plane. The differential operator of an arbitrary model equation of higher order can be represented as a product of polyanalytic and polyharmonic operators. The important step in in... |

5 |
A hierarchy of integral operators
- Begehr, Hile
- 1997
(Show Context)
Citation Context ...e represented as a product of polyanalytic and polyharmonic operators. The important step in investigating boundary value problems for higher order model equations was made by H. Begehr and G.N. Hile =-=[19]-=- (see also [6]), who constructed the hierarchy of higher order Pompeiu operators Tm,n, defined for any pair (m,n) of integer numbers m, n such that m+n ≥ 0. Operators 6 Tm,n act on the space Lp(D;C), ... |

5 | Aguilaniu H, Semb H, Nyström T (2006) Elimination of damaged proteins during differentiation of embryonic stem cells. Proc Natl Acad Sci U S A 103: 7700–7705 - Hernebring, Brolen |

4 |
The main theorem of calculus in complex analysis
- Begehr
(Show Context)
Citation Context ...∂z, the Laplace operator ∂z∂z and the Bitsadze operator ∂ 2 z . The basic boundary value problems for complex partial differential equations have been considered for different particular domains, see =-=[2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 29, 32, 34, 41, 43, 44]-=-. They are explicitly solved as well for the inhomogeneous Cauchy-Riemann equation as for the Poisson equation. Among these particular domains the case of the unit disc is mostly considered and explai... |

4 |
Biharmonic Dirichlet Problems in Complex Analysis
- Six
- 2006
(Show Context)
Citation Context ...problem for the Poisson equation. The second approach is connected with the name of Almansi, who introduced a concept of polyharmonic Green functions for the unit disk [4] (see also [11], [12], [10], =-=[13]-=-). The Almansi biharmonic Green function is different from the one mentioned above in its boundary behavior. The complex analytic approach gives the possibility to construct Green functions in explici... |

4 |
Y.F.Wang A Dirichlet problem for polyharmonic functions
- Begehr
(Show Context)
Citation Context ...s. These are also potential operators. Other potential operators of this kind for higher order model operators are developed for certain simple domains and the boundary value problems are solved, see =-=[10, 11, 23, 24]-=-. In the present thesis the Cauchy-Riemann equation ∂zw = f and the Poisson equation ∂z∂zw = f in two particular domains are studied, namely a quarter ring and a half hexagon. The boundary of the quar... |

4 |
boundary value problem for the Poisson equation
- Begehr, Robin
(Show Context)
Citation Context ...∂z, the Laplace operator ∂z∂z and the Bitsadze operator ∂ 2 z . The basic boundary value problems for complex partial differential equations have been considered for different particular domains, see =-=[2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 29, 32, 34, 41, 43, 44]-=-. They are explicitly solved as well for the inhomogeneous Cauchy-Riemann equation as for the Poisson equation. Among these particular domains the case of the unit disc is mostly considered and explai... |

4 | The Schwarz problem for polyanalytic functions - Begehr |

4 |
Harmonic boundary value problems in half disc and half ring, Functiones et Approximatio
- Begehr
(Show Context)
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4 |
Boundary value problems. Pergamon Press, Oxford-New York-Paris
- Gakhov
- 1966
(Show Context)
Citation Context ...at method we shall attain our aim Gotfried Wilhelm von Leibniz The theory of complex boundary value problems originating from the work of B.Riemann [35] and D.Hilbert [31] and developed by F.D.Gakhov =-=[28]-=-, I.N.Muskhelishvili [33], I.N.Vekua [42], W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equations of arbitrary order is explored after the basic... |

3 |
Some Schwarz problems in a quarter plane
- Abdymanapov, Begehr, et al.
(Show Context)
Citation Context ... where some of the boundary sides are replaced by circular arcs e.g. half discs, quarter discs, half rings, disc sectors, lenses and lunes, see [18, 22, 26, 43]. Some polygonal domains are studied in =-=[1, 2, 14, 19, 29, 44]-=- etc. Multiply connected domains are also considered, e.g. ring domains, in particular a concentric ring domain [20, 41]. For certain of the domains mentioned above a method for constructing the Schwa... |

3 |
Boundary value problems for higher order complex partial differential equations
- Du
- 2008
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3 |
Boundary Value Problems for Complex Partial Differential Equations in a ring domain
- Vaitsiakhovich
- 2008
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3 | Combined integral representations. Advances in Analysis. - Begehr - 2003 |

3 |
Hybrid Green functions and related boundary value problems
- Begehr
(Show Context)
Citation Context ...onvolution of two polyharmonic Green functions of lower order. The convolution of Green functions of different kinds defines a hybrid Green function (the denotation was introduced by H. Begehr) [11], =-=[12]-=-. The results concerning boundary value problems for the polyharmonic equation are given in [22],[23] for the unit disk, and in [14] for the upper half plane. The differential operator of an arbitrary... |

3 | Vaitekhovich T. Iterated Dirichlet problem for the higher order Poisson equation. Le Matematiche, submitted
- Begehr
(Show Context)
Citation Context ...hile passing for simply to multiply connected domains. The present thesis contributes to the research subject initiated by Prof. Dr. H. Begehr and developed by his students and collaborates [1], [5] =-=[21]-=-, [29], [32], [37], [47], [48]. A systematic investigation of boundary value problems for complex partial differential equations of arbitrary order on the base of integral representation formulas was ... |

3 |
Lectures on partial and Pfaffian differential equations.
- Haack, Wendland
- 1969
(Show Context)
Citation Context ...mulated for these equations. 3.5.1 Dirichlet, Neumann and Robin problems for the Poisson equation The Dirichlet and Neumann problems for the Poisson equation are wellknown in the literature, see e.g. =-=[36]-=-, [50]. Here explicit solutions for these problems are specified for a ring domain. A Robin problem for the Poisson equation is posed and its solution is found in explicit form. Theorem 3.5.7. The Dir... |

3 | Itroduction to Functional Analysis. J.Wiley and - Taylor |

3 | HV (2007) The nature of systems biology, Trends Microbiol 15 - FJ, Westerhoff |

2 | A.B.Tungatarov, Four boundary value problems for the Cauchy-Riemann equation in a quarter plane - Abdymanapov, Harutyunyan - 2005 |

2 |
problem for complex differential equations
- Aksoy
- 2007
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2 | Boundary value problems for Bitsadze equation - Begehr |

2 |
boundary value problem for the Cauchy-Riemann operator
- Begehr, Robin
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2 |
Complex boundary value problems in a quarter plane
- Begehr, Harytyunyan
(Show Context)
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2 | Complex partial differential equations in a manner of I.N.Vekua
- Begehr
(Show Context)
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2 |
A polyharmonic Dirichlet problem of arbitrary order for complex plane domains, Further progress
- Begehr
- 2007
(Show Context)
Citation Context ...s. These are also potential operators. Other potential operators of this kind for higher order model operators are developed for certain simple domains and the boundary value problems are solved, see =-=[10, 11, 23, 24]-=-. In the present thesis the Cauchy-Riemann equation ∂zw = f and the Poisson equation ∂z∂zw = f in two particular domains are studied, namely a quarter ring and a half hexagon. The boundary of the quar... |

2 |
Boundary value problems for tri-harmonic functions in the unit disc
- Burgumbayeva
- 2009
(Show Context)
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2 |
Boundary value problems in complex analysis
- Prakash
- 2007
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2 |
Gesammelte mathematische Werke, herausgegeben von H.Weber, zweite Auflage
- Riemann
- 1892
(Show Context)
Citation Context ...ee from the start, and even prove, that following that method we shall attain our aim Gotfried Wilhelm von Leibniz The theory of complex boundary value problems originating from the work of B.Riemann =-=[35]-=- and D.Hilbert [31] and developed by F.D.Gakhov [28], I.N.Muskhelishvili [33], I.N.Vekua [42], W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equa... |

2 | Iteration of the Pompeiu integral operator and complex higher order equations - Begehr - 1999 |

2 |
About the uniqueness of the Dirichlet problem for elliptic partial differential equations.
- Bitsadze
- 1948
(Show Context)
Citation Context ...et problem for the Laplace operator (or which is equivalent, for harmonic functions) in the unit disk wzz = 0 in D, w = 0 on ∂D has only the trivial solution, see e.g. [7]. As A.V. Bitsadze has shown =-=[25]-=-, this is failed for the Dirichlet problem wz z = 0 in D, w = 0 in ∂D, (1.2) having constructed the infinite set of linearly independent solutions wk(z) = (1− |z|2)zk, k ∈ N. The complex differential ... |

2 |
Integraldarstellungen mit Greenschen Funktionen hoeherer Ordnung in Gebieten und Polygebieten
- Krausz
- 2005
(Show Context)
Citation Context ...imply to multiply connected domains. The present thesis contributes to the research subject initiated by Prof. Dr. H. Begehr and developed by his students and collaborates [1], [5] [21], [29], [32], =-=[37]-=-, [47], [48]. A systematic investigation of boundary value problems for complex partial differential equations of arbitrary order on the base of integral representation formulas was initiated by H. Be... |

2 | Steinsaltz D (2007) Damage segregation at fissioning may increase growth rates: A superprocess model, Theoretical Population BiologyVolume 71 - Evans - 2003 |

2 | Regulation of yeast replicative life span by TOR and - Kaeberlein, Steffen - 2005 |

2 | Austriaco JrNR, Guarente L - BK - 1994 |

2 | Is ageing as complex as it would appear? Ann - Kirkwood, Franceschi - 1992 |

1 |
Two basic boundary value problems for inhomogeneous Cauchy-Riemann equation in an infinite sector
- Akel
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1 |
A hierarchy of integral operators, Rocky Mountain J.Math.27
- Begehr
- 1997
(Show Context)
Citation Context ...2], W.Haack and W.Wendland [30] and others is still investigated. On one hand a theory for complex model equations of arbitrary order is explored after the basic fundamental solutions were approached =-=[15]-=-. On the other hand explicit solutions are found in many different particular domains. The explicit solutions are important not only for applications in engineering, mathematical physics, fluid dynami... |

1 |
Harmonic Dirichlet problem for some equilateral triangle
- Begehr
(Show Context)
Citation Context ...n will be used to prove the boundary behavior for solution of the Schwarz problem on the respective parts of ∂P+. These proofs are based on the Poisson kernel of half planes, see Section 4.1 and e.g. =-=[19]-=-. The essential part of the boundary integrals in the representation formulas (4.30), (4.34) and (4.43) are the Schwarz operators for P+ Skγ(z) = 1 2pii ∫ ∂P+ γ(ζ) ∑ m+n∈2Z 2[qkmn(ζ, z)− qkmn(ζ, 0)]dζ... |

1 |
How to find harmonic Green function in the plane
- Begehr
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1 |
functions, reflections and plane parqueting
- Begehr, Green
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1 |
The parqueting-reflection principle for constructing Green functions
- Begehr
- 2013
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1 |
boundary value problems for the Cauchy-Riemann and the Poisson equations in a quarter disc
- Costache
- 2009
(Show Context)
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1 |
complex boundary value problems in the upper half plane
- Gärtner
- 2006
(Show Context)
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1 |
Lectures on Plaffian differential equations
- Haack
- 1972
(Show Context)
Citation Context ...ory of complex boundary value problems originating from the work of B.Riemann [35] and D.Hilbert [31] and developed by F.D.Gakhov [28], I.N.Muskhelishvili [33], I.N.Vekua [42], W.Haack and W.Wendland =-=[30]-=- and others is still investigated. On one hand a theory for complex model equations of arbitrary order is explored after the basic fundamental solutions were approached [15]. On the other hand explici... |

1 |
and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Application
- Mityushev, Linear
- 1999
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1 | boundary value problems in a quarter ring domain, Adv.Pure Appl.Math - Shupeyeva |

1 | Boundary Value Problems for Complex Partial Differential Equations in Fan-Shaped domains,PhD thesis - Wang - 2011 |

1 |
Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle, J.Math.Anal.Appl.(2010). Zusammenfassung Diese Doktorarbeit ist der Untersuchung von einigen Grenzwertproblemen für komplexen partielle Differenzgleichungen im Viertelkreis und
- Wang
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1 |
Sull'integrazione dell'equatzione differenziale 42nu
- Almansi
(Show Context)
Citation Context ...solution of a certain Dirichlet problem for the Poisson equation. The second approach is connected with the name of Almansi, who introduced a concept of polyharmonic Green functions for the unit disk =-=[4]-=- (see also [11], [12], [10], [13]). The Almansi biharmonic Green function is different from the one mentioned above in its boundary behavior. The complex analytic approach gives the possibility to con... |

1 |
Biharmonic Green functions. Le Matematiche
- Begehr
(Show Context)
Citation Context ...as a convolution of two polyharmonic Green functions of lower order. The convolution of Green functions of different kinds defines a hybrid Green function (the denotation was introduced by H. Begehr) =-=[11]-=-, [12]. The results concerning boundary value problems for the polyharmonic equation are given in [22],[23] for the unit disk, and in [14] for the upper half plane. The differential operator of an arb... |

1 |
Kernel Functions. Longman Scientific and Technical
- Begehr, Transformations, et al.
- 1992
(Show Context)
Citation Context ...iptic equations with constant or analytic coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], =-=[15]-=-, [30], [33], [34], [40], [49], [51], [52]. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundar... |

1 |
Zhang Z.-X. Polyharmonic Dirichlet problems
- Begehr, Vu
(Show Context)
Citation Context ...different kinds defines a hybrid Green function (the denotation was introduced by H. Begehr) [11], [12]. The results concerning boundary value problems for the polyharmonic equation are given in [22],=-=[23]-=- for the unit disk, and in [14] for the upper half plane. The differential operator of an arbitrary model equation of higher order can be represented as a product of polyanalytic and polyharmonic oper... |

1 |
Singular Partial Differential Equations. Boca Raton
- Dzhuraev
- 2000
(Show Context)
Citation Context ...equations with constant or analytic coefficients etc., and are connected with such names as N.I. Muskhelishvili, I.N. Vekua, F.D. Gakhov, J. Garnett, G.-C. Wen, A. Dzhuraev, H. Begehr, see [5], [15], =-=[30]-=-, [33], [34], [40], [49], [51], [52]. Boundary value problems were mostly considered in simply connected domains, i.e. unit disk, a half plane, a corner etc. The intention to investigate boundary valu... |

1 | Boundary Behavior of Conformal Maps. BerlinHeidelberg-New York-London - Ch - 1992 |

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Boundary value problems to second order complex partial differential equations in a ring domain
- Vaitekhovich
(Show Context)
Citation Context ...to multiply connected domains. The present thesis contributes to the research subject initiated by Prof. Dr. H. Begehr and developed by his students and collaborates [1], [5] [21], [29], [32], [37], =-=[47]-=-, [48]. A systematic investigation of boundary value problems for complex partial differential equations of arbitrary order on the base of integral representation formulas was initiated by H. Begehr. ... |

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Boundary value problems to first order complex partial differential equations in a ring domain
- Vaitekhovich
(Show Context)
Citation Context ...tiply connected domains. The present thesis contributes to the research subject initiated by Prof. Dr. H. Begehr and developed by his students and collaborates [1], [5] [21], [29], [32], [37], [47], =-=[48]-=-. A systematic investigation of boundary value problems for complex partial differential equations of arbitrary order on the base of integral representation formulas was initiated by H. Begehr. To sta... |

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