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

2019/01/03 by Bahrouni, Sabri, Ounaies, Hichem, Tavares, Leandro S. · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.00784

Abstract

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∈ (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.

Cited by

• On the singular elliptic problem involving the variable order fractional Musielak g_x,y-Laplacian
• Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters
• Comparison principle for Singular Fractional g- Laplacian Problems

Related

• Introduction to fractional Orlicz-Sobolev spaces
• Embedding theorems in the fractional Orlicz-Sobolev space and\n applications to non-local problems
• Ground state solutions for a non-local type problem in fractional Orlicz Sobolev spaces
• Remarks on a nonlinear nonlocal operator in Orlicz spaces
• Fractional order Orlicz-Sobolev spaces