Regularity for Shape Optimizers: The Nondegenerate Case. Issue 8 (13th February 2018) - Kriventsov, Dennis; Lin, Fanghua
Abstract: We consider minimizers of 1 F ( λ 1 ( Ω ), …, λ N ( Ω ) ) + | Ω |, where F is a function strictly increasing in each parameter, and λ k ( Ω ) is the k th Dirichlet eigenvalue of Ω. Our main result is that the reduced boundary of the minimizer is composed of C 1, 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.© 2018 Wiley Periodicals, Inc.