Regularity for Shape Optimizers: The Degenerate Case

Dennis Kriventsov, Fanghua Lin

We consider minimizers of \[ F(λ_1(Ω),\ldots,λ_N(Ω)) + |Ω|, \] where $F$ is a function nondecreasing in each parameter, and ${\lambda }_k(\Omega )$ is the $k$-th Dirichlet eigenvalue of $\Omega$. This…