9 papers · 1 filter
On the -Laplacian Quadrature Surface Free Boundary Problem on Riemannian Manifolds: Sufficient condition of existence
Mohammed Barkatou
We study the -Laplacian quadrature surface free boundary problem on a compact Riemannian manifold $(\M,g)$ of dimension , for . Given a nonnegative source…
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 . Given a positive source $f \in L^2_g(\M)$ with compact supp…
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 . Let be a compact strictly convex core, and $Ω\in \mathcal{O}_{…
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…
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…
Thickness functions for elliptic level sets: gradient formulas, normal expansions, and geometric remarks
Mohammed Barkatou
We study the geometry of superlevel sets of solutions to with compactly supported in a convex core . Under the radial monotonicit…
The Return Map in the Class : Geometry, Dynamics, and Thickness Regularity
Mohammed Barkatou, Mohamed El Morsalani
We study a discrete dynamical system on the boundary of a convex core , generated by linking to an outer boundary vi…
Existence of free boundaries for some overdetermined-value problems
Mohammed Barkatou
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the over…
Existence and Symmetry results for some overdetermined free boundary problems
Mohammed Barkatou
In this paper, we prove that a domain which verifies some integral inequality is either (strictly) contained in the solution of some free boundary problem, or it coincides with an…