1. A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional.
- Author
-
Babadjian, Jean-François, Millot, Vincent, and Rodiac, Rémy
- Subjects
- *
BRITTLE fractures - Abstract
This note addresses the question of convergence of critical points of the Ambrosio–Tortorelli functional in the one-dimensional case under pure Dirichlet boundary conditions. An asymptotic analysis argument shows the convergence to two possible limits points: either a globally affine function or a step function with a single jump at the middle point of the space interval, which are both critical points of the one-dimensional Mumford–Shah functional under a Dirichlet boundary condition. As a byproduct, non minimizing critical points of the Ambrosio–Tortorelli functional satisfying the energy convergence assumption as in (Babadjian, Millot and Rodiac (2022)) are proved to exist. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF