Monotone variations of the first eigenvalue for doubly connected domains
Chie‐Ping Chu, Chih Chy Fwu · Mathematische Nachrichten · 2003
Abstract The first Dirichlet eigenvalue for the Laplace operator of a doubly connected plane domain varies with the relative position of the inner hole. Under certain mild hypothesis it decreases as the two boundary curves get closer along some specific direction. We made this observation by analyzing level curves and rearrangement technique.