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

2011/02/19 by Changfeng Gui, Gui, Changfeng
Mathematics · #35J20 #35J60 #35J91 49Q05 #53A04 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Meromorphic and Entire Functions #Nonlinear Partial Differential Equations #math.AP #msc:35J20 #msc:35J60 #msc:35J91 #msc:49Q05 #msc:53A04

paper · pdf · doi:10.48550/arxiv.1102.4022

arxiv created 2011/02/19 · openalex publication_date 2011/02/19 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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