Every singular solution to a nonlocal linear equation with measurable kernel that is one-sided bounded near zero and infinity must equal a multiple of the fundamental solution plus a constant.
Singularities of solutions of nonlocal nonlinear equations
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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.
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Liouville theorem for singular solutions to nonlocal equations
Every singular solution to a nonlocal linear equation with measurable kernel that is one-sided bounded near zero and infinity must equal a multiple of the fundamental solution plus a constant.