Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones

Details Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones

2011-02-16

arxiv.org/abs/1102.3446v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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