Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones
Analysis of PDEs
2011-02-18 v1
Abstract
In this paper, we are interested in bounded, entire, solutions of the Allen-Cahn equation which are defined in Euclidean space and whose zero set is asymptotic to a given minimal cone. In particular, in dimension larger than or equal to 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes.
Cite
@article{arxiv.1102.3446,
title = {Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones},
author = {Frank Pacard and Juncheng Wei},
journal= {arXiv preprint arXiv:1102.3446},
year = {2011}
}