A note on fractional supersolutions

Janne Korvenpää, Tuomo Kuusi, Giampiero Palatucci

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Abstract

We study a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order s ϵ (0,1) and summability growth p > 1, whose model is the fractional p-Laplacian with measurable coefficients. We prove that the minimum of the corresponding weak supersolutions is a weak supersolution as well.

Original languageEnglish
Pages (from-to)1-9
JournalELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
Volume2016
Issue number263
Publication statusPublished - 28 Sep 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional Laplacian
  • Fractional Sobolev spaces
  • Fractional superharmonic functions
  • Nonlocal tail
  • Quasilinear nonlocal operators

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  • Cite this

    Korvenpää, J., Kuusi, T., & Palatucci, G. (2016). A note on fractional supersolutions. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016(263), 1-9.