Analysis on the junctions of domain walls

Luis A. Caffarelli, Fang Hua Lin

Research output: Contribution to journalArticlepeer-review


In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

Original languageEnglish (US)
Pages (from-to)915-929
Number of pages15
JournalDiscrete and Continuous Dynamical Systems
Issue number3
StatePublished - Nov 2010


  • Calculus of variations
  • Free boundaries
  • Montonicity formula

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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