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Mohamed Berghout

Publications and source records attributed to Mohamed Berghout.

9 recordsLinked to original sources
arXiv2025

On the singular elliptic problem involving the variable order fractional Musielak $g_{x,y}$-Laplacian

In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool is variational approach, however, various auxiliary tools from the theory of nonlinear functional analysis, convex analysis and critical point theory are also applied.

math.AP↗
arXiv2024

Theory of capacities in fracional Sobolev spaces with variable exponents

In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including monotonicity, outer capacity and several results, are studies. We prove that both capacities is a Choquet capacity and all borel sets are capacitable.

math.FA↗
arXiv2024

Some approximation properties in fractional Musielak-Sobolev spaces

In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev setting. The proofs of these properties are mainly based on a basic technique of convolution, joined with a cutoff, with some care needed in order not to exceed the original support.

math.FA↗
arXiv2023

On the Continuous embeddings between the fractional Hajłasz-Orlicz-Sobolev spaces

Let $G$ be an Orlicz function and let $ α, β, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces defined on metric-measure spaces $W_s^{α, G}(X, d, μ)$ and the fractional Hajłasz-Orlicz-Sobolev spaces $M^{β, G}(X,d,μ)$.

math.FA↗
arXiv2020

Fractional variable exponents Sobolev trace spaces

We introduce and study fractional variable exponents Sobolev trace spaces on any open set in the Euclidean space equipped with the Lebesgue measure. We show that every equivalence class of Sobolev functions has a quasicontinuous representatives. We use the relative capacity to characterize completely the zero trace fractional variable exponents Sobolev spaces. We also give a relative capacity criterium for removable sets.

math.FA↗