Abstract

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet--Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the $p$-torsional rigidity functional for $p \geq 2$.

Keywords

  1. shape functionals
  2. infimum problems
  3. domain derivative
  4. duality

MSC codes

  1. 49Q10
  2. 49K10
  3. 49M29
  4. 49J45

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1056 - 1084
ISSN (online): 1095-7138

History

Submitted: 21 January 2015
Accepted: 12 February 2016
Published online: 21 April 2016

Keywords

  1. shape functionals
  2. infimum problems
  3. domain derivative
  4. duality

MSC codes

  1. 49Q10
  2. 49K10
  3. 49M29
  4. 49J45

Authors

Affiliations

Funding Information

GNAMPA : N/A
University of Toulon- FRANCE : N/A

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