Regularity for Shape Optimizers: The Nondegenerate Case

Dennis Kriventsov, Fang-Hua Lin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
JournalCommunications on Pure and Applied Mathematics
DOIs
StateAccepted/In press - Jan 1 2018

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Minimizer
Regularity
Dirichlet Eigenvalues
Free Boundary Problem
Hausdorff Dimension
Bernoulli
Strictly
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Regularity for Shape Optimizers : The Nondegenerate Case. / Kriventsov, Dennis; Lin, Fang-Hua.

In: Communications on Pure and Applied Mathematics, 01.01.2018.

Research output: Contribution to journalArticle

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