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arXiv:1102.4022 [math.AP]AbstractReferencesReviewsResources

Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two Dimensions

Changfeng Gui

Published 2011-02-19Version 1

In this paper, we prove even symmetry and monotonicity of certain solutions of Allen-Cahn equation in a half plane. We also show that entire solutions with {\it finite Morse index} and {\it four ends} must be evenly symmetric with respect to two orthogonal axes. A classification scheme of general entire solutions with {\it finite Morse index} is also presented using energy quantization.

Categories: math.AP
Subjects: 35J20, 35J60, 35J91, 49Q05, 53A04
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