04-189 Berardino Sciunzi, Enrico Valdinoci

Mean curvature properties for $p$-Laplace phase transitions (472K, PostScript) Jun 17, 04

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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 global solutions of $\Delta_p u=h_0'(u)$ with some uniform limit properties satisfy a mean curvature equation in a suitable viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.

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