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.
Mean curvature properties for p-Laplace phase transitions / B. Sciunzi, E. Valdinoci. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 7:3(2005), pp. 319-359.
Mean curvature properties for p-Laplace phase transitions
E. ValdinociUltimo
2005
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 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.File | Dimensione | Formato | |
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