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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.
@article{COCV_2004__10_1_99_0,
author = {Briancon, Tanguy},
title = {Regularity of optimal shapes for the {Dirichlet's} energy with volume constraint},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {99--122},
publisher = {EDP-Sciences},
volume = {10},
number = {1},
year = {2004},
doi = {10.1051/cocv:2003038},
zbl = {1118.35078},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003038/}
}
TY - JOUR AU - Briancon, Tanguy TI - Regularity of optimal shapes for the Dirichlet's energy with volume constraint JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 99 EP - 122 VL - 10 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003038/ DO - 10.1051/cocv:2003038 LA - en ID - COCV_2004__10_1_99_0 ER -
%0 Journal Article %A Briancon, Tanguy %T Regularity of optimal shapes for the Dirichlet's energy with volume constraint %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 99-122 %V 10 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003038/ %R 10.1051/cocv:2003038 %G en %F COCV_2004__10_1_99_0
Briancon, Tanguy. Regularity of optimal shapes for the Dirichlet's energy with volume constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 99-122. doi: 10.1051/cocv:2003038
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