Some symmetry results for entire solutions of an elliptic system arising\n in phase separation

2013/07/21 by Alberto Farina, Farina, Alberto
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1307.5537

openalex publication_date 2013/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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