From the 1 of 9 linked papers with an AI index.
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Geometric Gradient Flows from Elliptic Level Sets: Normal Decomposition and Reflection Dynamics
Mohammed Barkatou, Mohamed El Morsalani
We investigate the asymptotic geometry of shifting superlevel sets generated by solutions to the elliptic Dirichlet problem in , wher…
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 monoto…
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…
The Return Map in the Class : Geometry, Dynamics, and Thickness Regularity
Mohammed Barkatou, Mohamed El Morsalani
We investigate a geometric dynamical mechanism arising in the class of domains containing a fixed convex set and satisfying two geometric normals properties int…
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…