Mean curvature properties for $p$-Laplace phase transitions

Sciunzi, 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 -