Mean curvature properties for p-Laplace phase transitions

Berardino Sciunzi; Enrico Valdinoci

doi:10.4171/JEMS/31

Mean curvature properties for p-Laplace phase transitions

Berardino Sciunzi, Enrico Valdinoci

Research output: Contribution to journal › Article

16 Citations (Scopus)

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 h₀ with suitable growth conditions. We prove that level sets of solutions of Δ_pu = 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.

Original language	English
Pages (from-to)	319-359
Number of pages	41
Journal	Journal of the European Mathematical Society
Volume	7
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/31
Publication status	Published - 1 Jan 2005
Externally published	Yes

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