Mean curvature properties for \(p\)-Laplace phase transitions (Q2388672)

Summary: 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.