# Mean curvature properties for $p$-Laplace phase transitions

Berardino Sciunzi; Enrico Valdinoci

Journal of the European Mathematical Society (2005)

- Volume: 007, Issue: 3, page 319-359
- ISSN: 1435-9855

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topSciunzi, Berardino, and Valdinoci, Enrico. "Mean curvature properties for $p$-Laplace phase transitions." Journal of the European Mathematical Society 007.3 (2005): 319-359. <http://eudml.org/doc/277654>.

@article{Sciunzi2005,

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 $\Delta _pu=h^\{\prime \}_0(u)$ 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.},

author = {Sciunzi, Berardino, Valdinoci, Enrico},

journal = {Journal of the European Mathematical Society},

keywords = {Ginzburg–Landau–Allen–Cahn phase transition models; geometric and qualitative properties of solutions; $p$-Laplacian operator; sliding methods},

language = {eng},

number = {3},

pages = {319-359},

publisher = {European Mathematical Society Publishing House},

title = {Mean curvature properties for $p$-Laplace phase transitions},

url = {http://eudml.org/doc/277654},

volume = {007},

year = {2005},

}

TY - JOUR

AU - Sciunzi, Berardino

AU - Valdinoci, Enrico

TI - Mean curvature properties for $p$-Laplace phase transitions

JO - Journal of the European Mathematical Society

PY - 2005

PB - European Mathematical Society Publishing House

VL - 007

IS - 3

SP - 319

EP - 359

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 $h_0$ with suitable growth conditions. We prove that level sets of solutions of $\Delta _pu=h^{\prime }_0(u)$ 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.

LA - eng

KW - Ginzburg–Landau–Allen–Cahn phase transition models; geometric and qualitative properties of solutions; $p$-Laplacian operator; sliding methods

UR - http://eudml.org/doc/277654

ER -

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