Radial symmetry of ground states for a regional fractional nonlinear schrödinger equation

Abstract

The aim of this paper is to study radial symmetry properties for ground state solutions of elliptic equations involving a regional fractional Laplacian, namely (-[delta])[alfa][ro][ípsilon]+u = f(u)in Rn, for [alfa] [épsilon](0,1). In [9], the authors proved that problem (1) has a ground state solution. In this work we prove that the ground state level is achieved by a radially symmetry solution. The proof is carried out by using variational methods jointly with rearrangement arguments.