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

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    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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    Elliptic Equations
    Rigidity
    Lipschitz
    Monotonicity
    Fractional
    Regularity
    Nonlocal Equations
    Unbounded Domain
    Half-space
    Infinity
    Symmetry

    Cite this

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    title = "On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results",
    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).",
    author = "Serena Dipierro and Nicola Soave and Enrico Valdinoci",
    year = "2017",
    month = "12",
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    language = "English",
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    pages = "1283–1326",
    journal = "Mathematische Annalen",
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    On fractional elliptic equations in Lipschitz sets and epigraphs : regularity, monotonicity and rigidity results. / Dipierro, Serena; Soave, Nicola; Valdinoci, Enrico.

    In: Mathematische Annalen, Vol. 369, No. 3-4, 12.2017, p. 1283–1326.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - On fractional elliptic equations in Lipschitz sets and epigraphs

    T2 - regularity, monotonicity and rigidity results

    AU - Dipierro, Serena

    AU - Soave, Nicola

    AU - Valdinoci, Enrico

    PY - 2017/12

    Y1 - 2017/12

    N2 - 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).

    AB - 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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    U2 - 10.1007/s00208-016-1487-x

    DO - 10.1007/s00208-016-1487-x

    M3 - Article

    VL - 369

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    EP - 1326

    JO - Mathematische Annalen

    JF - Mathematische Annalen

    SN - 0025-5831

    IS - 3-4

    ER -