Symmetry results for cooperative elliptic systems in unbounded domains

2012/12/19 by Lucio Damascelli, Francesca Gladiali, Damascelli, Lucio +3
Computer Science · Mathematics · #35B06 #35B50 #35G60 #35J47 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1212.4647

openalex publication_date 2012/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove symmetry results for classical solutions of semilinear cooperative elliptic systems in R^N, or in the exterior of a ball. We consider the case of fully coupled systems and nonlinearities which are either convex or have a convex derivative. The solutions are shown to be foliated Schwarz symmetric if a bound on their Morse index holds. As a consequence of the symmetry results we also obtain some nonexistence theorems.

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