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Regularity for nonlocal equations with local Neumann boundary conditions

Regularity for nonlocal equations with local Neumann boundary conditions

In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,\gamma}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v \asymp d^{s-1}$ and are sometimes called large solutions. In this setup we prove …