SOME SYMMETRY RESULTS FOR ENTIRE SOLUTIONS OF AN ELLIPTIC SYSTEM ARISING IN PHASE SEPARATION

被引：12

作者：

Farina, Alberto ^{[1
,2
]}

机构：

[1] Univ Picardie Jules Verne, LAMFA, CNRS, UMR 7352, F-80039 Amiens, France

[2] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 06期

关键词：

Symmetry results for elliptic systems; entire solutions; Almgrens monotonicity formulae;

D O I：

10.3934/dcds.2014.34.2505

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the one dimensional symmetry of entire solutions to an elliptic system arising in phase separation for Bose-Einstein condensates with multiple states. We prove that any monotone solution, with arbitrary algebraic growth at infinity, must be one dimensional in the case of two spatial variables. We also prove the one dimensional symmetry for half-monotone solutions, i.e., for solutions having only one monotone component.

引用

页码：2505 / 2511

页数：7

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