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

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    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).

    Original languageEnglish
    Pages (from-to)1283–1326
    Number of pages44
    JournalMathematische Annalen
    Volume369
    Issue number3-4
    DOIs
    Publication statusPublished - Dec 2017

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