Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators

TL;DR

This paper proves foliated Schwarz symmetry for solutions to a cooperative nonlocal system, including fractional Laplacian cases, and provides an explicit example demonstrating the applicability of the results.

Contribution

It establishes symmetry results for solutions to a broad class of nonlocal cooperative systems, extending known symmetry results to fractional and other nonlocal operators.

Findings

Solutions exhibit foliated Schwarz symmetry

Applicable to fractional Laplacian and similar operators

Includes explicit example of a nonlocal nonlinear system

Abstract

In this paper, we prove foliated Schwarz symmetry of solutions to a cooperatively coupled system of equations involving nonlocal operators. Here, the class of nonlocal operators covers in particular the case of the fractional Laplacian. Moreover, we give an explicit example of a nonlocal nonlinear system, in which our result can be applied.