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

By S. Bahrouni, Hichem Ounaies, L. S. Tavares. Topological Methods in Nonlinear Analysis, 2019

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In this paper, we study the interplay between Orlicz-Sobolev spaces $L^{M}$ and $W^{1,M}$ and fractional Sobolev spaces $W^{s,p}$. More precisely, we give some qualitative properties of the new fractional Orlicz-Sobolev space $W^{s,M}$, where $s\in (0,1)$ and $M$ is an $N-$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 weak solution for a non-local problem involving the new fractional $M-$Laplacian operator.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

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