Overdetermined elliptic problems in nontrivial exterior domains of the hyperbolic space

Guowei Dai, Pieralberto Sicbaldi, Yong Zhang

We construct nontrivial unbounded domains $\Omega$ in the hyperbolic space ${\mathbb{H}}^N$, $N\in \{2,3,4\}$, bifurcating from the complement of a ball, such that the overdetermined ell…