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 › peer-review

17 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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keywords = "Geometric and qualitative properties of solutions, Ginzburg-Landau-Allen-Cahn phase transition models, p-Laplacian operator, Sliding methods",

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AB - 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 Δpu = 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.

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KW - Ginzburg-Landau-Allen-Cahn phase transition models

KW - p-Laplacian operator

KW - Sliding methods

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Mean curvature properties for p-Laplace phase transitions

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