Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations

Janne Korvenpää, Tuomo Kuusi*, Giampiero Palatucci

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)

Abstract

We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order (Formula presented.) and summability growth (Formula presented.), whose model is the fractional p-Laplacian with measurable coefficients. We state and prove several results for the corresponding weak supersolutions, as comparison principles, a priori bounds, lower semicontinuity, and many others. We then discuss the good definition of (s, p)-superharmonic functions, by also proving some related properties. We finally introduce the nonlocal counterpart of the celebrated Perron method in nonlinear Potential Theory.

Original languageEnglish
Pages (from-to)1443–1489
Number of pages47
JournalMATHEMATISCHE ANNALEN
Volume369
Issue number3-4
DOIs
Publication statusPublished - Dec 2017
MoE publication typeA1 Journal article-refereed

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