M. Barkatou

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20202026

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7 papers · 2 filters

math.AP2026

On the $p$ -Laplacian Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient condition of existence

Mohammed Barkatou

We study the $p$ -Laplacian quadrature surface free boundary problem on a compact Riemannian manifold $(\M,g)$ of dimension $N \geq 2$ , for $1 < p < \infty$ . Given a nonnegative source…

math.AP2026

On the Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient Condition of Existence

Mohammed Barkatou

We study the quadrature surface free boundary problem on a compact Riemannian manifold $(\M,g)$ of dimension $N \geq 2$ . Given a positive source $f \in L^2_g(\M)$ with compact supp…

math.AP2026

Elliptic Superlevel Sets in the Class $\OO_C$: Boundary-Layer Geometry and Stability of the Return Map

Mohammed Barkatou, Mohamed El Morsalani, Mohammd Barkatou

We study elliptic superlevel geometry and return dynamics for the class $O_{C}$ . Let $C \subset R^{N}$ be a compact strictly convex core, and $Ω\in \mathcal{O}_{…

math.AP2026

Sharp existence conditions and geometric inheritance for overdetermined free boundary problems of Laplacian and bi-Laplacian type

Mohammed Barkatou, Samira Khatmi

This paper provides necessary and sufficient conditions for the existence of free boundaries in overdetermined problems for the Laplacian, and sufficient conditions for the bi-Lapl…

math.AP2026

Symmetry and Qualitative \& Quantitative Stability for a Class of Overdetermined Problems in C-GNP Domains with Source Supported in the Core

Mohammed Barkatou

We introduce a unified geometric framework for domains satisfying a geometric normal property (C-GNP) relative to a strictly convex set $C$. Under the fundamental assumption that…

math.AP2026

Thickness functions for elliptic level sets: gradient formulas, normal expansions, and geometric remarks

Mohammed Barkatou

We study the geometry of superlevel sets $Ω_{t} = {u > t}$ of solutions to $- Δ u = μ$ with $μ \geq 0$ compactly supported in a convex core $C \subset Ω$ . Under the radial monotonicit…

math.AP2026

The Return Map in the Class $O_{C}$ : Geometry, Dynamics, and Thickness Regularity

Mohammed Barkatou, Mohamed El Morsalani

We study a discrete dynamical system $F = π \circ Φ$ on the boundary of a convex core $\partial C \subset R^{N}$ , generated by linking $C$ to an outer boundary $\partial Ω$ vi…

On the p-Laplacian Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient condition of existence

On the Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient Condition of Existence

Elliptic Superlevel Sets in the Class $\OO_C$: Boundary-Layer Geometry and Stability of the Return Map

Sharp existence conditions and geometric inheritance for overdetermined free boundary problems of Laplacian and bi-Laplacian type

Symmetry and Qualitative \& Quantitative Stability for a Class of Overdetermined Problems in C-GNP Domains with Source Supported in the Core

Thickness functions for elliptic level sets: gradient formulas, normal expansions, and geometric remarks

The Return Map in the Class OC​: Geometry, Dynamics, and Thickness Regularity

On the $p$ -Laplacian Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient condition of existence

The Return Map in the Class $O_{C}$ : Geometry, Dynamics, and Thickness Regularity