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

ESAIM: Control, Optimisation and Calculus of Variations (2004)

- Volume: 10, Issue: 1, page 99-122
- ISSN: 1292-8119

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topBriancon, Tanguy. "Regularity of optimal shapes for the Dirichlet’s energy with volume constraint." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2004): 99-122. <http://eudml.org/doc/245908>.

@article{Briancon2004,

abstract = {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.},

author = {Briancon, Tanguy},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {shape optimization; calculus of variations; free boundary; geometrical measure theory; Shape optimization},

language = {eng},

number = {1},

pages = {99-122},

publisher = {EDP-Sciences},

title = {Regularity of optimal shapes for the Dirichlet’s energy with volume constraint},

url = {http://eudml.org/doc/245908},

volume = {10},

year = {2004},

}

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

PB - EDP-Sciences

VL - 10

IS - 1

SP - 99

EP - 122

AB - 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.

LA - eng

KW - shape optimization; calculus of variations; free boundary; geometrical measure theory; Shape optimization

UR - http://eudml.org/doc/245908

ER -

## References

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