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math.AP2016
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 }…
math.AP2016
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 , …
math.AP2016
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…