Research Communication | Open Access
Volume 2019 | Communication ID 22
Volume 2019 | Communication ID 22
| An introduction to generalized fractional Sobolev Space with variable exponent |
Mohammed Shimi, Elhoussine Azroul, Abdelmoujib Benkirane
Received |
Accepted |
Published |
Dec 12, 2018 |
Dec 31, 2018 |
Mar 01, 2019 |
Abstract: In this paper, we extend the fractional Sobolev spaces with variable exponents $W^{s,p(x,y)}$ to include the general fractional case $W^{K,p(x,y)}$, where $p$ is a variable exponent, $s\in (0,1)$ and $K$ is a suitable kernel. We are concerned with some qualitative properties of the space $W^{K,p(x,y)}$ (completeness, reflexivity, separability and density). Moreover, we prove a continuous embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we establish the existence and uniqueness of a solution for a non-local problem involving the non-local ...