Regularity for Shape Optimizers: The Nondegenerate Case

Dennis Kriventsov, Fanghua Lin

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