Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spaces
Advances in Operator Theory - 2020
Tóm tắt
In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz–Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend the fractional Sobolev spaces
$$W^{s,p}$$
to include the general case
$$W^sL_A$$
, where A is an N-function and
$$s\in (0,1)$$
. We are concerned with some qualitative properties of the space
$$W^sL_A$$
(completeness, reflexivity and separability). Moreover, we prove a continuous and compact embedding theorem of these spaces into Lebesgue spaces.
Từ khóa
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