Janne Korvenpaa, Tuomo Kuusi, Giampiero Palatucci
Abstract:
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 coefficients. We prove that the minimum of the corresponding
weak supersolutions is a weak supersolution as well.
Submitted September 8, 2016. Published September 28, 2016.
Math Subject Classifications: 35D10, 35B45, 35B05, 35R05, 47G20, 60J75.
Key Words: Quasilinear nonlocal operators; fractional Sobolev spaces;
fractional Laplacian; nonlocal tail; fractional superharmonic functions.
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| Janne Korvenpaa Department of Mathematics and Systems Analysis Aalto University P.O. Box 1100 00076 Aalto, Finland email: janne.korvenpaa@aalto.fi | |
| Tuomo Kuusi Department of Mathematics and Systems Analysis Aalto University P.O. Box 1100 00076 Aalto, Finland email: tuomo.kuusi@aalto.fi | |
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Giampiero Palatucci Dipartimento di Matematica e Informatica Universita degli Studi di Parma Campus - Parco Area delle Scienze, 53/A 43124 Parma, Italy email: giampiero.palatucci@unipr.it |
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