Fractional superharmonic functions and the Perron method for nonlinear\n integro-differential equations

2016/05/03 by Janne Korvenpää, Tuomo Kuusi, Korvenpaa, Janne +3 · 6 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1605.00906

openalex publication_date 2016/05/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We deal with a class of equations driven by nonlocal, possibly degenerate,\nintegro-differential operators of differentiability order s\∈ (0,1) and\nsummability growth p>1, whose model is the fractional p-Laplacian with\nmeasurable coefficients. We state and prove several results for the\ncorresponding weak supersolutions, as comparison principles, a priori bounds,\nlower semicontinuity, and many others. We then discuss the good definition of\n(s,p)-superharmonic functions, by also proving some related properties. We\nfinally introduce the nonlocal counterpart of the celebrated Perron method in\nnonlinear Potential Theory.\n

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