Nontrivial solutions to the relative overdetermined torsion problem in a cylinder

Filomena Pacella, David Ruiz, Pieralberto Sicbaldi

Given a bounded regular domain $\omega \subset {\mathbb{R}}^{N-1}$ and the half-cylinder $\Sigma =\omega \times (0,+\infty )$, we consider the relative overdetermined torsion problem in $\Sigma$, i.e. \[\l…