Mean curvature properties for p-Laplace phase transitions

Berardino Sciunzi, Enrico Valdinoci

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Pages (from-to)319-359
Number of pages41
JournalJournal of the European Mathematical Society
Volume7
Issue number3
DOIs
Publication statusPublished - 1 Jan 2005
Externally publishedYes

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Mean Curvature
Laplace
Phase Transition
Phase transitions
Viscosity
Level-set Approach
Double-well Potential
Kinetics
P-Laplacian
Growth Conditions
Level Set
Hypersurface
Decay
Zero
Energy

Cite this

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Mean curvature properties for p-Laplace phase transitions. / Sciunzi, Berardino; Valdinoci, Enrico.

In: Journal of the European Mathematical Society, Vol. 7, No. 3, 01.01.2005, p. 319-359.

Research output: Contribution to journalArticle

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AU - Valdinoci, Enrico

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