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

By Serena Dipierro, Nicola Soave, Enrico Valdinoci. 2016

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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. These results can be seen as the nonlocal counterpart of the celebrated article (Berestycki et al., Commun Pure Appl Math 50(11):1089–1111, 1997).

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9f10132cce2dfb6afe86813380ab61fd22e05698