Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation

The aim of this paper is to study radial symmetry properties for ground state solutions of elliptic equations involving a regional fractional Laplacian, namely\begin{eqnarray}(-\Delta)_{\rho}^{\alpha}u + u = f(u) \quad \mbox{in} \ \mathbb{R}^{n}, \ \ \mbox{for} \ \ \alpha\in (0,1).\end{eqnarray}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.