Singularities of solutions of nonlocal nonlinear equations

Abstract

We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution.

Proof of 1-dimemsional case has been fixed. 39 pages