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An introduction to generalized fractional Sobolev Space with variable exponent. (arXiv:1901.05687v1 [math.AP])
来源于:arXiv
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 nonlocal problem involving the nonlocal integrodifferential
operator of elliptic type. 查看全文>>