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Briancon, Tanguy
Regularity of optimal shapes for the Dirichlet’s energy with volume constraint. ESAIM: Control, Optimisation and Calculus of Variations, 10 no. 1 (2004), p. 99-122
Texte intégral djvu | pdf | Analyses Zbl 1118.35078 | 1 citation dans Numdam
Class. Math.: 35R35, 49N60, 49Q10
Mots clés: shape optimization, calculus of variations, free boundary, geometrical measure theory

URL stable: http://www.numdam.org/item?id=COCV_2004__10_1_99_0

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Résumé

In this paper, we prove some regularity results for the boundary of an open subset of $\mathbb{R}^d$ 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.

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