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

Fingerprint

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

Sciunzi, B., & Valdinoci, E. (2005). Mean curvature properties for p-Laplace phase transitions. Journal of the European Mathematical Society, 7(3), 319-359. https://doi.org/10.4171/JEMS/31

Sciunzi, Berardino ; Valdinoci, Enrico. / Mean curvature properties for p-Laplace phase transitions. In: Journal of the European Mathematical Society. 2005 ; Vol. 7, No. 3. pp. 319-359.

@article{6d4c0e1c0ba044769c1adfffe7ebb097,

title = "Mean curvature properties for p-Laplace phase transitions",

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.",

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

author = "Berardino Sciunzi and Enrico Valdinoci",

year = "2005",

month = "1",

day = "1",

doi = "10.4171/JEMS/31",

language = "English",

volume = "7",

pages = "319--359",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "3",

}

Sciunzi, B & Valdinoci, E 2005, 'Mean curvature properties for p-Laplace phase transitions' Journal of the European Mathematical Society, vol. 7, no. 3, pp. 319-359. https://doi.org/10.4171/JEMS/31

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 journal › Article

TY - JOUR

T1 - Mean curvature properties for p-Laplace phase transitions

AU - Sciunzi, Berardino

AU - Valdinoci, Enrico

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

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.

KW - Geometric and qualitative properties of solutions

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

KW - p-Laplacian operator

KW - Sliding methods

UR - http://www.scopus.com/inward/record.url?scp=23744502733&partnerID=8YFLogxK

U2 - 10.4171/JEMS/31

DO - 10.4171/JEMS/31

M3 - Article

VL - 7

SP - 319

EP - 359

JO - Journal of the European Mathematical Society