Regularity for Shape Optimizers: The Nondegenerate Case

Dennis Kriventsov, Fanghua Lin

Research output: Contribution to journalArticlepeer-review


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)
Pages (from-to)1535-1596
Number of pages62
JournalCommunications on Pure and Applied Mathematics
Issue number8
StatePublished - Aug 2018

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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