This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of -Laplacian type and a double well potential with suitable growth conditions. We prove that level sets of solutions of 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.
Cite this article
Berardino Sciunzi, Enrico Valdinoci, Mean curvature properties for p-Laplace phase transitions. J. Eur. Math. Soc. 7 (2005), no. 3, pp. 319–359DOI 10.4171/JEMS/31