| Issue |
ESAIM: COCV
Volume 10, Number 1, January 2004
|
|
|---|---|---|
| Page(s) | 99 - 122 | |
| DOI | https://doi.org/10.1051/cocv:2003038 | |
| Published online | 15 February 2004 | |
Regularity of optimal shapes for the Dirichlet's energy with volume constraint
1
Université Rennes 1.
2
Antenne de Bretagne de l'École Normale Supérieure
de Cachan; briancon@bretagne.ens-cachan.fr.
Received:
25
February
2003
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
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