Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

S. Chanillo, D. Grieser, M. Imai +2

We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega \subset {\mathbb{R}}^n$ and numbers $\alpha \ge 0$, $A\in [0,|\Omega |]$, find a subset $D\subset \Omega$ of area $A$ for wh…