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The Dirichlet Problem for the Total Variation Flow
, 2001
"... We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L¹ for entropy solutions. To prove the existence we u ..."
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Cited by 27 (9 self)
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We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L¹ for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions.
A.: Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment
 Comput. Optim. App
, 2011
"... Abstract: An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed prob ..."
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Cited by 3 (1 self)
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Abstract: An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.
PERIODIC SOLUTIONS FOR A NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
"... Abstract. In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with ..."
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Abstract. In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with the Schauder fixed point theorem. 1.
function that is not polyconvex M. Silhavy THEORETICAL AND APPLIED MECHANICS
"... An O(n) invariant nonnegative rank 1 convex function of linear growth is given that is not polyconvex. This answers a recent question [8, p. 182] and [5]. The polyconvex hull of the function is calculated explicitly if n = 2: 1 ..."
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An O(n) invariant nonnegative rank 1 convex function of linear growth is given that is not polyconvex. This answers a recent question [8, p. 182] and [5]. The polyconvex hull of the function is calculated explicitly if n = 2: 1
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"... ftp ejde.math.swt.edu (login: ftp) Strongly nonlinear parabolic initialboundary value problems in Orlicz spaces ∗ ..."
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ftp ejde.math.swt.edu (login: ftp) Strongly nonlinear parabolic initialboundary value problems in Orlicz spaces ∗