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On Inversion of Fractional Spherical Potentials by Spherical Hypersingular Operators
, 2002
"... A new proof of the inversion formula for spherical Riesz type fractional potentials in the case 0 < <α < 2 is presented and a constructive reduction of the case <α> 2 to the case 0 < <α < 2 is given. 1. ..."
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A new proof of the inversion formula for spherical Riesz type fractional potentials in the case 0 < <α < 2 is presented and a constructive reduction of the case <α> 2 to the case 0 < <α < 2 is given. 1.
Fractional and hypersingular operators in variable exponent spaces on metric measure spaces
 MEDITERRANEAN JOURNAL OF MATHEMATICS
, 2008
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Iterative Substructuring for hVersion Boundary Element Approximation of the Hypersingular Operator in Three Dimensions ∗
"... Additive Schwarz preconditioners are developed for the hversion of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The first preconditioner consists of decomposing into local spaces associated with the subdomain interiors, supplemented with a w ..."
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Additive Schwarz preconditioners are developed for the hversion of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The first preconditioner consists of decomposing into local spaces associated with the subdomain interiors, supplemented with a
Digital Object Identifier (DOI) 10.1007/s002110000134 Numer. Math. (2000) 85: 343–366 Numerische Mathematik
"... for pversion boundary element approximation of the hypersingular operator in three dimensions? ..."
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for pversion boundary element approximation of the hypersingular operator in three dimensions?
Fractional integrals and hypersingular integrals in variable order Hölder . . .
, 2009
"... We consider nonstandard Hölder spaces Hλ(·)(X) of functions f on a metric measure space (X, d, µ), whose Hölder exponent λ(x) is variable, depending on x ∈ X. We establish theorems on mapping properties of potential operators of variable order α(x), from such a variable exponent Hölder space wit ..."
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Cited by 4 (2 self)
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of the local continuity modulus of potential and hypersingular operators via such modulus of their densities. These estimates allow us to treat not only the case of the spaces Hλ(·)(X), but also the generalized Hölder spaces Hw(·,·)(X) of functions whose continuity modulus is dominated by a given function w
KOLMOGOROV TYPE INEQUALITIES FOR HYPERSINGULAR INTEGRALS WITH HOMOGENEOUS CHARACTERISTIC
"... Abstract. New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of multivariate functions from Hölder spaces are obtained. Proved inequalities are used to solve the Stechkin’s problem on the best approximation of unbounded hypersingular integral operat ..."
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Abstract. New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of multivariate functions from Hölder spaces are obtained. Proved inequalities are used to solve the Stechkin’s problem on the best approximation of unbounded hypersingular integral
The Numerical Solution of a Nonlinear Hypersingular Boundary Integral Equation
"... In this paper we consider a direct hypersingular integral approach to solve harmonic problems with nonlinear boundary conditions by using a practical variant of the Galerkin boundary element method. The proposed approach provides an almost optimal balance between the order of convergence and the num ..."
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and the numerical e#ort of work to compute the approximate solution. Numerical examples confirm the theoretical results. Subject Classification: AMS (MOS) 65F35, 65N22, 65N38. Key Words: Boundary element methods, nonlinear boundary conditions, hypersingular integral operator. 1 Introduction Boundary integral
A Multigrid Method on Graded Meshes for a Hypersingular Integral Equation
"... Introduction The multigrid method has been successfully applied to a large variety of problems, see e.g., [4]. One of the most important applications is the fast solution of linear systems arising from elliptic boundary value problems, e.g., by di#erence methods, or by using finite elements. Another ..."
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in exterior domains, and the simple generation of the meshes. Since the multigrid theory has been formulated for elliptic operators in a very abstract framework [9, 10], it is possible to obtain convergence of the multigrid method for some elliptic boundary integral equations, see [5, 14]. In these papers a
A multiresolution approach to regularization of singular operators and fast summation
 SIAM J. Sci. Comp
, 2002
"... Abstract. Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide numerical procedures for constructing or ..."
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Abstract. Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide numerical procedures for constructing
Minimizing the StrayField Energy in Micromagnetics Subject to a Pointwise Constraint
"... The boundary element method (BEM) with hypersingular operators on open surfaces is used to approximate the solutions to Neumann problems for elliptic operators of second order in exterior domains. The solutions of problems on open surfaces typically exhibit a singular behavior at the edges and corn ..."
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The boundary element method (BEM) with hypersingular operators on open surfaces is used to approximate the solutions to Neumann problems for elliptic operators of second order in exterior domains. The solutions of problems on open surfaces typically exhibit a singular behavior at the edges
Results 1  10
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42