Regularity of optimal shapes for the Dirichlet's energy with volume constraint
Université Rennes 1.
2 Antenne de Bretagne de l'École Normale Supérieure de Cachan; firstname.lastname@example.org.
Revised: 4 August 2003
In this paper, we prove some regularity results for the boundary of an open subset of 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.
Mathematics Subject Classification: 35R35 / 49N60 / 49Q10
Key words: Shape optimization / calculus of variations / free boundary / geometrical measure theory.
© EDP Sciences, SMAI, 2004