A new class of fractional Orlicz-Sobolev space and singular elliptic problems

This paper seeks to introduce a new class of fractional Orlicz-Sobolev space with variable-order. We give basic properties of this space and prove some compactness results. Then, using some techniques of calculus of variations combined with theory of Musielak functions, we prove the existence of a nonnegative weak solution for a singular elliptic type problem in a fractional variable-order Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces a new class of fractional Orlicz-Sobolev space with variable-order. The basic properties of this space are given and some compactness results are proved. Then, using techniques of calculus of variations combined with the theory of Musielak functions, the existence of a nonnegative weak solution for a singular elliptic type problem in a fractional variable-order Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions is proved. (c) 2023 Elsevier Inc. All rights reserved.