Weak uniqueness and partial regularity for the composite membrane problem

Sagun Chanillo, Carlos E. Kenig

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler-Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler-Lagrange equations.

Original languageEnglish (US)
Pages (from-to)705-737
Number of pages33
JournalJournal of the European Mathematical Society
Volume10
Issue number3
DOIs
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Composite membrane
  • Free boundary
  • Monotonicity formula
  • Partial regularity
  • Uniqueness

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