论文标题
嵌入和扩展会导致分数Musielak-Sobolev空间
Embedding and extension results in Fractional Musielak-Sobolev spaces
论文作者
论文摘要
在本文中，我们关注了新的Musielak-Sobolev空间的某些定性特性$ W^SL _ {\ varphi_ {\ varphi_ {x，y}} $，使得Poincaré类型不平等和某些连续且紧凑的嵌入这些空间的定理。此外，我们证明$ W^sl _ {\ varphi_ {x，y}}}（ω）$中的任何功能都可以扩展到$ w^sl _ {\ varphi_ {\ varphi_ {x，y}}}（\ r^n）$中的函数，带有$ c \ subset \ subset \ r^n $ and and a $ c and a $ c^c^n $ c^c^n $ c^c^n $ c^c^0.此外，我们建立了一个与$ w^s {l _ {\ varphi_ {x，y}}}} \ left（\ r^n \ right）$的互补子空间有关的结果。作为应用程序，使用山区通过定理和一些变异方法，我们研究了具有DIRICHLET边界数据的一类非局部分数类型问题的非平凡弱解。
In this paper, we are concerned with some qualitative properties of the new fractional Musielak-Sobolev spaces $W^sL_{\varPhi_{x,y}}$ such that the generalized Poincaré type inequality and some continuous and compact embedding theorems of these spaces. Moreover, we prove that any function in $W^sL_{\varPhi_{x,y}}(Ω)$ may be extended to a function in $W^sL_{\varPhi_{x,y}}(\R^N)$, with $Ω\subset \R^N$ is a bounded domain of class $C^{0,1}$. In addition, we establish a result relates to the complemented subspace in $W^s{L_{\varPhi_{x,y}}}\left( \R^N\right)$. As an application, using the mountain pass theorem and some variational methods, we investigate the existence of a nontrivial weak solution for a class of nonlocal fractional type problems with Dirichlet boundary data.
