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

Antoine Laurain (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients

A. Piatnitski, A. Rybalko, V. Rybalko (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We study the first eigenpair of a Dirichlet spectral problem for singularly perturbed convection-diffusion operators with oscillating locally periodic coefficients. It follows from the results of [A. Piatnitski and V. Rybalko, On the first eigenpair of singularly perturbed operators with oscillating coefficients. Preprint www.arxiv.org, arXiv:1206.3754] that the first eigenvalue remains bounded only if the integral curves of the so-called effective drift have a nonempty ω-limit set. Here we consider...

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