A rigidity result for overdetermined elliptic problems in the plane

Antonio Ros, David Ruiz, Pieralberto Sicbaldi

Let $f:[0,+\infty )\to \mathbb{R}$ be a (locally) Lipschitz function and $\Omega \subset {\mathbb{R}}^2$ a $C^{1,\alpha }$ domain whose boundary is unbounded and connected. If there exists a pos…