5 citations · 7 across the 14 of their papers we have counts for
17 papers
Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
We use shape derivative approach to prove that balls are the only convex and regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begi…
An Overdetermined Neumann boundary value problem with a general driving force
Ignace Aristide Minlend, Jing Wu
In this paper, we prove the existence of a family of non trivial compact subdomains in the manifold for which the overdetermined Neuma…
Overdetermined problems with sign-changing eigenfunctions in unbounded periodic domains
Ignace Aristide Minlend
We prove the existence of nontrivial unbounded domains in the Euclidean space for which the Dirichlet eigenvalue problem for the Laplacian on admits sign-changing ei…
Exceptional domains in higher dimensions
Ignace Aristide Minlend, Tobias Weth, Jing Wu
We prove the existence of nontrivial unbounded exceptional domains in the Euclidean space , . These domains arise as perturbations of complements of straight cylinder…
The Schiffer problem on the cylinder and on the -sphere
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We prove the existence of a family of compact subdomains of the flat cylinder for which the Neumann eigenvalue problem for the Lapl…
An overdetermined problem for sign-changing eigenfunctions in unbounded domains
Ignace Aristide Minlend
We study the existence of non-trivial unbounded domains of where the equation \begin{align} - λu_{xx} -u_{tt} &= u \qquad \text{in ,}\nonumber u &=0 \qqu…
On an electrostatic problem and a new class of exceptional subdomains of
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We study the existence of nontrivial unbounded surfaces with the property that the constant charge distribution on is an electrostatic equilibrium, i.e.…
Unbounded periodic constant mean curvature graphs on Calibrable Cheeger Serrin domains
Ignace Aristide Minlend
We prove a general result characterizing a specific class of Serrin domains as supports of unbounded and periodic constant mean curvature graphs. We apply this result to prove the…
Overdetermined problems for fully nonlinear equations in space forms
Ignace Aristide Minlend
We study overdetermined problems for fully nonlinear elliptic equations in subdomains of the Euclidean sphere and the hyperbolic space . We pro…
Foliation of an asymptotically flat end by critical capacitors
Mouhammed Moustapha Fall, Ignace Aristide Minlend, Jesse Ratzkin
We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. Thes…
Multiply-periodic hypersurfaces with constant nonlocal mean curvature
Ignace Aristide Minlend, Alassane Niang, El Hadji Abdoulaye Thiam
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constrain…
Serrin's overdetermined problem on the sphere
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We study Serrin's overdetermined boundary value problem \begin{equation*} -Δ_{S^N}\, u=1 \quad \text{ in },\qquad u=0, \; \partial_ηu=\textrm{const} \quad \text{on }…
Existence of Self-Cheeger Sets on Riemannian Manifolds
Ignace Aristide Minlend
Let be a compact Riemannian manifold of dimension . We prove the existence of a family of self-Chee…
Unbounded periodic solutions to Serrin's overdetermined boundary value problem
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We study the existence of nontrivial unbounded domains in such that the overdetermined problem $$ -Δu = 1 \quad \text{in }, \qquad u=0, \quad \partial_νu=\tex…
Existence of Self-Cheeger sets on Riemannian manifolds
Ignace Aristide Minlend
Let be a compact Riemannian manifold of dimension . We prove the existence of a family of self-Cheeg…
The role of the mean curvature in a Hardy-Sobolev trace inequality
Mouhamed Moustapha Fall, Ignace Aristide Minlend, El Hadji Abdoulaye Thiam
The Hardy-Sobolev trace inequality can be obtained via Harmonic extensions on the half-space of the Stein and Weiss weighted Hardy-Littlewood-Sobolev inequality. In this paper we c…
Serrin's over-determined Problem on Riemannian Manifolds
Mouhamed Moustapha Fall, Ignace Aristide Minlend
Let be a compact Riemannian manifold of dimension , . In this paper, we prove that there exists a family of domains $(Ω_\varepsilon)_{\varepsilon\in(0…