Basic results of fractional Orlicz-Sobolev space and applications to non-local problems

Sabri Bahrouni, Hichem Ounaies, Leandro S. Tavares



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 $s\in (0,1)$ 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.


Fractional Orlicz-Sobolev space; fractional $M$-Laplacian; non-local problems; existence of solution

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