We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order s∈(0,1) and
summability growth p>1, 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.Comment: To appear in Math. An