Nonlocal problems with Neumann and Robin boundary condition in fractional Musielak-Sobolev spaces

2022/03/03 by Elhoussine Azroul, Azroul, Elhoussine, Abdelmoujib Benkirane +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2203.01756

openalex publication_date 2022/03/03 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop some properties of the a_x,y(.)-Neumann derivative for the fractional a_x,y(.)-Laplacian operator. Therefore we prove the basic proprieties of the correspondent function spaces. In the second part of this paper, by means of Ekeland's variational principal and direct variational approach, we prove the existence of weak solutions for a nonlocal problem with nonhomogeneous Neumann and Robin boundary condition.

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