An isoperimetric result for an energy related to the $p$-capacity

Abstract

In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $\Omega$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $\Omega$ are concentric balls. We use the $H$-function and a derearrangement technique.

References in corpus (3)

• A free boundary problem in thermal insulation with a prescribed heat source
• A free boundary problem for the p-Laplacian with nonlinear boundary conditions
• Shape optimization for a nonlinear elliptic problem related to thermal insulation