Calculus of Variations and Geometric Measure Theory

J. Korvenpaa - T. Kuusi - G. Palatucci

A note on fractional supersolutions

created by palatucci on 29 Oct 2016


Published Paper

Inserted: 29 oct 2016
Last Updated: 29 oct 2016

Journal: Electron. J. Differential Equations
Volume: 2016
Number: 263
Pages: 1-9
Year: 2016


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

Keywords: fractional Laplacian, fractional Sobolev spaces, quasilinear nonlocal operators, nonlocal tail, Fractional Superharmonic functions