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).
On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results / S. Dipierro, N. Soave, E. Valdinoci. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 369:3-4(2017 Dec), pp. 1283-1326. [10.1007/s00208-016-1487-x]
On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
S. DipierroPrimo
;E. ValdinociUltimo
2017
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. 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).
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