Basic results of fractional Orlicz-Sobolev space and applications to non-local problems - Bahrouni, Sabri; Ounaies, Hichem; Tavares, Leandro S. (Topological Methods in Nonlinear Analysis, 2020)
In this paper, we study the interplay between the Orlicz-Sobolev spaces L^M and W^1,M and the fractional Sobolev spaces W^s,p. More precisely, we give some qualitative properties of a new fractional Orlicz-Sobolev space W^s,M, where s(0,1) and M is a Young function. We also study a related non-local operator, which is a fractional version of the nonhomogeneous M-Laplace operator. As an application, we prove existence of a weak solution for a non-local problem involving the new fractional M-Laplacian operator.