Global minimizer of the ground state for two phase conductors in low contrast regime
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, p. 362-388

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.

DOI : https://doi.org/10.1051/cocv/2013067
Classification:  49Q10,  35P15,  49R05,  47A55,  34E10
Keywords: shape optimization, eigenvalue optimization, two-phase conductors, low contrast regime, asymptotic analysis
@article{COCV_2014__20_2_362_0,
     author = {Laurain, Antoine},
     title = {Global minimizer of the ground state for two phase conductors in low contrast regime},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {2},
     year = {2014},
     pages = {362-388},
     doi = {10.1051/cocv/2013067},
     zbl = {1287.49047},
     mrnumber = {3264208},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2014__20_2_362_0}
}
Laurain, Antoine. Global minimizer of the ground state for two phase conductors in low contrast regime. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, pp. 362-388. doi : 10.1051/cocv/2013067. http://www.numdam.org/item/COCV_2014__20_2_362_0/

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