# Global minimizer of the ground state for two phase conductors in low contrast regime

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 2, page 362-388
- ISSN: 1292-8119

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topLaurain, Antoine. "Global minimizer of the ground state for two phase conductors in low contrast regime." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 362-388. <http://eudml.org/doc/272805>.

@article{Laurain2014,

abstract = {The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue in low contrast regime is either a centered ball or the union of a centered ball and of a centered ring touching the boundary, depending on the prescribed volume ratio between the two materials.},

author = {Laurain, Antoine},

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

keywords = {shape optimization; eigenvalue optimization; two-phase conductors; low contrast regime; asymptotic analysis},

language = {eng},

number = {2},

pages = {362-388},

publisher = {EDP-Sciences},

title = {Global minimizer of the ground state for two phase conductors in low contrast regime},

url = {http://eudml.org/doc/272805},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Laurain, Antoine

TI - Global minimizer of the ground state for two phase conductors in low contrast regime

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 2

SP - 362

EP - 388

AB - The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue in low contrast regime is either a centered ball or the union of a centered ball and of a centered ring touching the boundary, depending on the prescribed volume ratio between the two materials.

LA - eng

KW - shape optimization; eigenvalue optimization; two-phase conductors; low contrast regime; asymptotic analysis

UR - http://eudml.org/doc/272805

ER -

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