Regularity for Shape Optimizers: The Nondegenerate Case
Dennis Kriventsov, Fanghua Lin
Source abstract
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 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.
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