arXiv subjects

Abdeslem Lyaghfouri

Publications and source records attributed to Abdeslem Lyaghfouri.

8 recordsLinked to original sources

arXiv2024

Porosity of the Free Boundary in a Class of Higher-Dimensional Elliptic Problems

We investigate a class of n-dimensional free boundary elliptic problems which includes the dam problem, the aluminum problem, and the lubrication problem. We establish that the free boundary in this class is a porous set, which implies its Hausdorff dimension being less than $n$, which in turn leads to its Lebesgue measure being zero. Our proof relies on the comparison of the solution with an appropriately constructed barrier function.

math.AP↗

arXiv2022

Lipschitz Continuity for Elliptic Free Boundary Problems with Dini Mean Oscillation Coefficients

We establish local interior Lipschitz continuity of the solutions of a class of free boundary elliptic problems assuming the coefficients of the equation of Dini mean oscillation in at least one direction. The novelty in this regularity result lies in the fact that it allows discontinuous coefficients in all but one variable.

math.AP↗

arXiv2021

Global Higher Integrability of the Gradient of the A-Laplace Equation Solution

In this paper, we establish higher integrability of the gradient of the solution of the quasilinear elliptic equation $Δ_Au=\text{div}\left(\frac{a(|F|)}{|F|}F\right)$ in $\mathbb{R}^n$, where $Δ_Au$ is the so called A-Laplace operator.

math.AP↗

arXiv2019

A Note on Lipschitz Continuiy of the Solutions of a Class of Elliptic Free Boundary Problems

We provide a new and simple proof based on Harnack's inequality to the Lipschitz continuity of the solutions of a class of free boundary problems.

math.AP↗

arXiv2019

Continuity of the Free Boundary in a Problem involving the A-Laplacian

In this paper we investigate a two dimensional free boundary problem involving the A-Laplacian. We show that the free boundary is represented locally by graphs of a family of continuous functions.

math.AP↗

arXiv2019

A class of free boundary problems with Neuman boundary condition

In this work, we investigate the continuity of the free boundary in a class of elliptic problems, with Neuman boundary condition. The main idea is a change of variable that allows us to reduce the problem to the one studied in [14].

math.AP↗

arXiv2015

Porosity of the Free Boundary in the Singular p-Parabolic Obstacle Problem

In this paper we establish the exact growth of the solution of the singular quasilinear p-parabolic obstacle problem near the free boundary from which we deduce its porosity.

math.AP↗

arXiv2015

Uniqueness of Solution of the Unsteady Filtration Problem in Heterogeneous Porous Media

We establish uniqueness of the solution of the unsteady state dam problem in the heterogeneous and rectangular case assuming the dam wet at the bottom and dry near to the top.

math.AP↗