Mean curvature properties for p-Laplace phase transitions

• Autores: Berardino Sciunzi , Enrico Valdinoci
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 7, Nº 3, 2005, págs. 319-360
• Idioma: inglés
• DOI: 10.4171/jems/31
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• Resumen

  • 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.