A note on fractional supersolutions

Janne Korvenpää; Tuomo Kuusi; Giampiero Palatucci

A note on fractional supersolutions

Janne Korvenpää
, Tuomo Kuusi
, Giampiero Palatucci

Department of Mathematics and Systems Analysis

University of Parma

Research output: Contribution to journal › Article › Scientific › peer-review

9 Citations (Scopus)

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 language	English
Pages (from-to)	1-9
Journal	Electronic Journal of Differential Equations
Volume	2016
Issue number	263
Publication status	Published - 28 Sept 2016
MoE publication type	A1 Journal article-refereed

Keywords

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

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https://ejde.math.txstate.edu/Volumes/2016/263/abstr.html

Cite this

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title = "A note on fractional supersolutions",

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.",

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T1 - A note on fractional supersolutions

AU - Korvenpää, Janne

AU - Kuusi, Tuomo

AU - Palatucci, Giampiero

PY - 2016/9/28

Y1 - 2016/9/28

N2 - 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.

AB - 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.

KW - Fractional Laplacian

KW - Fractional Sobolev spaces

KW - Fractional superharmonic functions

KW - Nonlocal tail

KW - Quasilinear nonlocal operators

UR - https://www.scopus.com/pages/publications/84989211338

M3 - Article

AN - SCOPUS:84989211338

SN - 1550-6150

VL - 2016

SP - 1

EP - 9

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

IS - 263

ER -

A note on fractional supersolutions

Abstract

Keywords

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