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Regularity of optimal shapes for the Dirichlet's energy with volume constraint

Published online by Cambridge University Press:  15 February 2004

Tanguy Briancon
Tanguy Briancon*
Affiliation:
Université Rennes 1. Antenne de Bretagne de l'École Normale Supérieure de Cachan; briancon@bretagne.ens-cachan.fr.
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Abstract

In this paper, we prove some regularity results for the boundary of an open subset of $\xR^d$ which minimizes the Dirichlet's energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.

Keywords

Shape optimizationcalculus of variationsfree boundarygeometrical measure theory.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 1 , January 2004 , pp. 99 - 122
Copyright
© EDP Sciences, SMAI, 2004

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