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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 99-122. <http://eudml.org/doc/90723>.

@article{Briancon2010,

abstract = {
In this paper, we prove some
regularity results for the boundary of an open subset of
$\xR^d$ 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.; free boundary; geometrical measure theory},

language = {eng},

month = {3},

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/90723},

volume = {10},

year = {2010},

}

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

DA - 2010/3//

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
$\xR^d$ 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.; free boundary; geometrical measure theory

UR - http://eudml.org/doc/90723

ER -

## References

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- M. Hayouni, Existence et régularité pour des problèmes d'optimisation de formes. Ph.D. thesis, université Henri Poincaré Nancy 1 (1997).
- M. Hayouni, Lipschitz continuity of the state function in a shape optimization problem. J. Convex Anal.6 (1999) 71–90. Zbl0948.49021
- M. Hayouni, T. Briancon and M. Pierre. On a volume constrained shape optimization problem with nonlinear state equation. (to appear). Zbl1062.49035
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