Mean curvature properties for p-Laplace phase transitions

Abstract

This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of $p$-Laplacian type and a double well potential $h_0$ with suitable growth conditions. We prove that level sets of solutions of ${\Delta }_{p}u=h_0^{\prime }(u)$ possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.