On the optimal shape of a thin insulating layer

Abstract

We are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\epsilon h$, where $h$ is a non-negative function defined on the boundary $\partial \Omega$. We study the problem in the limit for $\epsilon$ going to zero using a first-order asymptotic development by $\Gamma$-convergence.

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