Regularity for Shape Optimizers: The Nondegenerate Case
Dennis Kriventsov, Fanghua Lin · Communications on Pure and Applied Mathematics · 2018
Abstract We consider minimizers of urn:x-wiley:0010-3640:media:cpa21743:cpa21743-math-0001 where F is a function strictly increasing in each parameter, and 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.© 2018 Wiley Periodicals, Inc.