Regularity for Shape Optimizers: The Nondegenerate Case. Issue 8 (13th February 2018)

• Record Type: Journal Article
• Authors: Kriventsov, Dennis; Lin, Fanghua
• Is Part Of: Communications on pure and applied mathematics. Volume 71:Issue 8(2018:Aug.)
• Page Start: 1535
• Page End: 1596
• Publication Date: 2018-02-13
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21743
• Languages: English
• ISSNs: 0010-3640

Abstract

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.