On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results

preprint2016arXivOpen access

Abstract

We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity.

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