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Variational approach to shape derivatives

Published online by Cambridge University Press:  07 February 2008

Kazufumi Ito ,
Karl Kunisch  and
Gunther H. Peichl
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA; kito@unity.ncsu.edu
Karl Kunisch
Affiliation:
Institute for Mathematics and Scientific Computing, Karl-Franzens-University Graz, 8010 Graz, Austria; karl.kunisch@uni-graz.at; gunther.peichl@uni-graz.at
Gunther H. Peichl
Affiliation:
Institute for Mathematics and Scientific Computing, Karl-Franzens-University Graz, 8010 Graz, Austria; karl.kunisch@uni-graz.at; gunther.peichl@uni-graz.at
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Abstract

A general framework for calculating shape derivatives foroptimization problems with partial differential equations asconstraints is presented. The proposed technique allows to obtainthe shape derivative of the cost without the necessity to involvethe shape derivative of the state variable. In fact, the statevariable is only required to be Lipschitz continuous with respectto the geometry perturbations. Applications to inverse interfaceproblems, and shape optimization for elliptic systems and theNavier-Stokes equations are given.

Keywords

Shape derivative
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 3 , July 2008 , pp. 517 - 539
Copyright
© EDP Sciences, SMAI, 2008

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