The obstacle problem for nonlinear integro-differential operators

Janne Korvenpää, Tuomo Kuusi, Giampiero Palatucci*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

22 Citations (Scopus)

Abstract

We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and Hölder continuity (up to the boundary), from the obstacle.

Original languageEnglish
Article number63
Pages (from-to)1-29
JournalCalculus of Variations and Partial Differential Equations
Volume55
Issue number3
DOIs
Publication statusPublished - 1 Jun 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • 35B45
  • 35R05
  • 47G20
  • 60J75
  • Primary: 35D10
  • Secondary: 35B05

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