Regularity of the minimizers in the composite membrane problem in R2

Sagun Chanillo, Carlos E. Kenig, Tung To

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We study the regularity of the minimizers to the problem:λ (α, A) = under(inf, u ∈ H01 (Ω), {norm of matrix} u {norm of matrix}2 = 1, | D | = A) under(∫, Ω) | D u |2 + α under(∫, D) u2 . We prove that in the physical case α < λ in R2, any minimizer u is locally C1, 1 and the boundary of the set {u > c} is analytic where c is the constant such that D = {u < c} (up to a zero measure set).

Original languageEnglish (US)
Pages (from-to)2299-2320
Number of pages22
JournalJournal of Functional Analysis
Volume255
Issue number9
DOIs
StatePublished - Nov 1 2008

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Composite membrane
  • Domain variation
  • Free-boundary
  • Minimizer
  • Regularity

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