Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities (Q2453516)

In this paper the authors investigate the local behaviour of the nonnegative solutions of the equation \[ (-\Delta)^{\sigma}u=u^{\frac{n+2\sigma}{n-2\sigma}}\qquad {\text{ in}}\qquad B_1\backslash\{0\}, \] with an isolated singularity at the origin, the punctured unit ball \(B_1\backslash\{0\}\subset \mathbb R^n\) with \(n\geq 2\), \(\sigma\in (0, 1)\) and \((-\Delta)^{\sigma}\) is the fractional Laplacian. The authors prove that all solutions are asymptotically radially symmetric.