Critical points of ambrosio-tortorelli converge to critical points of Mumford-Shah in the one-dimensional dirichlet case

Gilles A. Francfort, Nam Q. Le, Sylvia Serfaty

Research output: Contribution to journalArticle


Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

Original languageEnglish (US)
Pages (from-to)576-598
Number of pages23
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number3
StatePublished - Jul 1 2009



  • Ambrosio-Tortorelli functional
  • Brittle fracture
  • Critical points
  • Gamma-convergence
  • Mumford-Shah functional

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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