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Sensitivity Analysis for a Class of \({{H_{0}^{1}}}\)-Elliptic Variational Inequalities of the Second Kind

  • Constantin Christof
  • Christian Meyer
Article
  • 11 Downloads

Abstract

We study the stability of solutions to \({H_{0}^{1}}\)-elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii operator. The local Lipschitz continuity of the solution map with respect to perturbations of the right-hand side and perturbations of the coefficient of the Nemytskii operator is proved for a large class of problems, and Hadamard directional differentiability results are obtained under comparatively mild structural assumptions. It is further shown that the directional derivatives of the solution map are typically characterized by elliptic variational inequalities in weighted Sobolev spaces whose bilinear forms contain surface integrals.

Keywords

Elliptic variational inequalities of the second kind Sensitivity analysis Hadamard directional differentiability Lipschitz stability Optimal control of variational inequalities 

Mathematics Subject Classification (2010)

35B30 35J20 35R45 47J20 49J40 49K40 65K15 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Chair of Optimal Control, Center for Mathematical SciencesTU MünchenGarchingGermany
  2. 2.Faculty of Mathematics, LSXTU DortmundDortmundGermany

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