We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order (Formula presented.) and summability growth (Formula presented.), whose model is the fractional p-Laplacian with measurable coefficients. We state and prove several results for the corresponding weak supersolutions, as comparison principles, a priori bounds, lower semicontinuity, and many others. We then discuss the good definition of (s, p)-superharmonic functions, by also proving some related properties. We finally introduce the nonlocal counterpart of the celebrated Perron method in nonlinear Potential Theory.

Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations / Korvenpää, Janne; Kuusi, Tuomo; Palatucci, Giampiero. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 369:3-4(2017), pp. 1-1443. [10.1007/s00208-016-1495-x]

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

PALATUCCI, Giampiero
2017

Abstract

We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order (Formula presented.) and summability growth (Formula presented.), whose model is the fractional p-Laplacian with measurable coefficients. We state and prove several results for the corresponding weak supersolutions, as comparison principles, a priori bounds, lower semicontinuity, and many others. We then discuss the good definition of (s, p)-superharmonic functions, by also proving some related properties. We finally introduce the nonlocal counterpart of the celebrated Perron method in nonlinear Potential Theory.
Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations / Korvenpää, Janne; Kuusi, Tuomo; Palatucci, Giampiero. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 369:3-4(2017), pp. 1-1443. [10.1007/s00208-016-1495-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2820398
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