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Equivalence of solutions to fractional p-Laplace type equations
Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland..
Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
2019 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 132, p. 1-26Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
ELSEVIER , 2019. Vol. 132, p. 1-26
Keywords [en]
Nonlocal operators, Fractional Sobolev spaces, Fractional p-Laplacian, Viscosity solutions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-266291DOI: 10.1016/j.matpur.2017.10.004ISI: 000500376300001Scopus ID: 2-s2.0-85074411859OAI: oai:DiVA.org:kth-266291DiVA, id: diva2:1383068
Note

QC 20200107

Available from: 2020-01-07 Created: 2020-01-07 Last updated: 2020-01-07Bibliographically approved

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Lindgren, Erik

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