Mean curvature properties for p-Laplace phase transitions

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'(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.