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arXiv · 2007.11043

Embedding and extension results in Fractional Musielak-Sobolev spaces

Elhoussine Azroul·Abdelmoujib Benkirane·Mohammed Shimi·Mohammed Srati
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Abstract

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 Poincar\'e type inequality and some continuous and compact embedding theorems of these spaces. Moreover, we prove that any function in $W^sL_{\varPhi_{x,y}}(\Omega)$ may be extended to a function in $W^sL_{\varPhi_{x,y}}(\R^N)$, with $\Omega \subset \R^N$ 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.

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Elhoussine Azroul, Abdelmoujib Benkirane, Mohammed Shimi, Mohammed Srati. 2020-07-21. Embedding and extension results in Fractional Musielak-Sobolev spaces. https://arxiv.org/abs/2007.11043

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