Some remarks about the summability of nonlocal nonlinear problems

In this note, we will study the problem {(-Delta)(p)(s)u = f(x) on Omega, u = 0 in R-N \ Omega, where 0 < s < 1, (-Delta)(p)(s) is the nonlocal p-Laplacian defined below, Omega is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [31] for the case p = 2 to the general case p epsilon ( 1, + infinity), the summability of the finite energy solutions in terms of the summability of a source term f(x). The aim of this note is to present the results in a way as elementary as possible.