We consider minimizers of F(λ1(Ω),...,λn(Ω))+|Ω| where F is a function strictly increasing in each parameter, and λk(Ω) is the kth Dirichlet eigenvalue of Ω. Our main result is that the reduced boundary of the minimizer is composed of C1,α graphs and exhausts the topological boundary except for a set of Hausdorff dimension at most n – 3. We also obtain a new regularity result for vector-valued Bernoulli-type free boundary problems.
ASJC Scopus subject areas
- Applied Mathematics