Author

M. Barkatou

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Preprint Sep 2026

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

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 support $K$, and $k>0$, one seeks a domain $\Omega \supset K$ on which the overdetermined problem $-\Delta_g u = f$ in $\Omega$, $u=0$ and $|\na...

M. Barkatou · 0 citations

Preprint Sep 2026

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

We study the $p$-Laplacian quadrature surface free boundary problem on a compact Riemannian manifold $(\M,g)$ of dimension $N \geq 2$, for $10$, one seeks a domain $\Omega \supset K$ on which the overdetermined problem $-\Delta_{p,g} u = f$ in $\Omega$, $u=0$ and $|\nabla_g u|_g = k$ on $\partial\Omega$ admits a soluti...

M. Barkatou · 0 citations