期刊
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
卷 132, 期 -, 页码 1-26出版社
ELSEVIER
DOI: 10.1016/j.matpur.2017.10.004
关键词
Nonlocal operators; Fractional Sobolev spaces; Fractional p-Laplacian; Viscosity solutions
资金
- Magnus Ehrnrooth Foundation [ma2014n1, ma2015n3]
- Academy of Finland [265007]
- Swedish Research Council [2012-3124]
- Academy of Finland (AKA) [265007, 265007] Funding Source: Academy of Finland (AKA)
In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional p-Laplace type P.V. integral(Rn)vertical bar u(x) - u(y)vertical bar(p-2)(u(x) - u(y))/vertical bar x-y vertical bar(n+sp) dy = 0. Solutions are defined via integration by parts with test functions, as viscosity solutions or via comparison. Our main result states that for bounded solutions, the three different notions coincide. (C) 2017 Elsevier Masson SAS. All rights reserved.
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