65 citations · 274 across the 61 of their papers we have counts for
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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 }…
Branch continuation inside the essential spectrum for the nonlinear Schrödinger equation
Gilles Evéquoz, Tobias Weth
We consider the nonlinear stationary Schrödinger equation \begin{equation*} -Δu -λu= Q(x)|u|^{p-2}u, \qquad \text{in }\mathbb{R}^N \end{equation*} in the case where , …
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…
Delaunay hypersurfaces with constant nonlocal mean curvature
Xavier Cabre, Mouhamed Moustapha Fall, Tobias Weth
We study hypersurfaces of with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter funct…