Solutions to overdetermined elliptic problems in nontrivial exterior domains

Antonio Ros, David Ruiz, Pieralberto Sicbaldi

In this paper we construct nontrivial exterior domains $\Omega \subset {\mathbb{R}}^N$, for all $N\ge 2$, such that the problem $$\left\{ {ll} -Δu +u -u^p=0,\ u >0 & \mbox{in }\; Ω, {1mm]…