Equivalence of solutions to fractional p-Laplace type equations

Janne Korvenpää, Tuomo Kuusi*, Erik Lindgren

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

18 Citations (Scopus)

Abstract

In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional p-Laplace type P.V.∫Rn [Formula presented] 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.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalJournal des Mathematiques Pures et Appliquees
Volume132
DOIs
Publication statusPublished - 1 Dec 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional p-Laplacian
  • Fractional Sobolev spaces
  • Nonlocal operators
  • Viscosity solutions

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