3 papers
math.AP2026
Existence, uniqueness and regularity of solutions to the parabolic Ambrosio-Tortorelli system
Martin Rakovsky
We investigate the existence, uniqueness, and regularity of the gradient flow of the Ambrosio-Tortorelli functional, viewed as an initial-boundary value problem, in arbitrary dimen…
math.AP2026
Critical points of the two-dimensional Ambrosio-Tortorelli functional with convergence of the phase-field energy
Jean-François Babadjian, Martin Rakovsky, Rémy Rodiac
We consider a family of critical points of the Ambrosio-Tortorelli functional. Assuming a uniform energy bound, the sequence $\…
math.AP2024
Critical points of the one dimensional Ambrosio-Tortorelli functional with an obstacle condition
Martin Rakovsky
We consider a family of critical points of the Ambrosio-Tortorelli energy with an obstacle condition on the phase field variable. This problem can be interpreted as a time discreti…