A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional

DOI10.3233/asy-231857zbMath1529.49024OpenAlexW4311661925MaRDI QIDQ6071961

Rémy Rodiac, Jean-François Babadjian, Vincent Millot

Publication date: 29 November 2023

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-231857

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)

Cites Work

• Unnamed Item
• Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term
• Optimal approximations by piecewise smooth functions and associated variational problems
• Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
• The Variational Approach to Fracture

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