2 problems

Let $\Omega \subset \mathbb{R}^d$ be a bounded domain, and consider the overdetermined elliptic problem referred to in the paper as equation, whose solution has constant forcing an…

First Schiffer conjecture D in $\mathbb{S}^2$. If such a solution exists, then $\Omega$ is a geodesic ball. The paper states that this first-eigenvalue version is true on…