M. Barkatou

activity

20202026

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11 papers · 1 filter

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.DS2026

Inverse Problems for the Return Map in the Class ( $O_{C}$ ): Reconstruction and Identifiability

Mohamed El Morsalani, Mohammed Barkatou

We study the inverse problem associated with the return map $F$ on the boundary of a convex core $C$ . By decomposing the return displacement into tangential and normal components,…

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.DS2026

Non-Autonomous Return Dynamics for Nested Convex Bodies:\\ Cubic Tangency, Summable Geometric Variation, and Critical Regimes

Mohamed El Morsalani, Mohammed Barkatou

We study a non-autonomous geometric dynamics generated by successive normal transitions between nested convex boundaries sharing a common tangency point. For \(C_{k+1}\subset C_k\s…

math.DS2026

Geometry, Dynamics, and Topology of the Thickness Landscape: A Morse-Theoretic Analysis of the Return Map in the Class $O_{C}$

Mohammed Barkatou, Mohamed El Morsalani

We study the geometry, dynamics, and topology of the thickness landscape associated with the geometric return map in the class $O_{C}$ . For a convex core $C$ and an admissib…

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.DS2026

Global Convergence Regimes of the Return Dynamics in the Class $O_{C}$

Mohammed Barkatou, Mohamed El Morsalani

This study investigates the global dynamics of discrete return maps $F : \partial C \to \partial C$ generated on the boundary of a convex core $C \subset R^{N}$ via an outwar…

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

Inverse Problems for the Return Map in the Class ( OC​ ): Reconstruction and Identifiability

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

Non-Autonomous Return Dynamics for Nested Convex Bodies:\\ Cubic Tangency, Summable Geometric Variation, and Critical Regimes

Geometry, Dynamics, and Topology of the Thickness Landscape: A Morse-Theoretic Analysis of the Return Map in the Class OC​

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

Global Convergence Regimes of the Return Dynamics in the Class OC​

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

Inverse Problems for the Return Map in the Class ( $O_{C}$ ): Reconstruction and Identifiability

Geometry, Dynamics, and Topology of the Thickness Landscape: A Morse-Theoretic Analysis of the Return Map in the Class $O_{C}$

Global Convergence Regimes of the Return Dynamics in the Class $O_{C}$

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