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arXiv:1102.3446 [math.AP]AbstractReferencesReviewsResources

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

Frank Pacard, Juncheng Wei

Published 2011-02-16Version 1

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.

Categories: math.AP
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