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

Abstract

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
Volume15
Issue number3
DOIs
StatePublished - Jul 2009

Fingerprint

Brittle fracture
Dirichlet
Critical point
Mumford-Shah Functional
Boundary conditions
Converge
Brittle Fracture
Elastic Material
Fidelity
Dirichlet Boundary Conditions
Symmetry
Term

Keywords

  • 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

Cite this

Critical points of ambrosio-tortorelli converge to critical points of Mumford-Shah in the one-dimensional dirichlet case. / Francfort, Gilles A.; Le, Nam Q.; Serfaty, Sylvia.

In: ESAIM - Control, Optimisation and Calculus of Variations, Vol. 15, No. 3, 07.2009, p. 576-598.

Research output: Contribution to journalArticle

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