Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

DOI10.1051/cocv:2008041zbMath1168.49041OpenAlexW2156686670MaRDI QIDQ5192127

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

Publication date: 4 August 2009

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/245594

zbMATH Keywords

brittle fracturecritical points\(\Gamma\)-convergenceMumford-Shah functionalAmbrosio-Tortorelli functional

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Nonlinear elliptic equations (35J60) Methods involving semicontinuity and convergence; relaxation (49J45) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (9)

Parameter selection in a Mumford-Shah geometrical model for the detection of thin structures ⋮ From gradient damage laws to Griffith's theory of crack propagation ⋮ A finer singular limit of a single-well Modica-Mortola functional and its applications to the Kobayashi-Warren-Carter energy ⋮ A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional ⋮ A variational model for plastic slip and its regularization via \(\Gamma \)-convergence ⋮ Unilateral gradient flow of the Ambrosio-Tortorelli functional by minimizing movements ⋮ The variational approach to fracture ⋮ A phase-field description of dynamic brittle fracture ⋮ Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics

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