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math.OC2025
Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
Matthieu Bonnivard, Elie Bretin, Antoine Lemenant +1
This work focuses on a phase field approximation of Plateau's problem. Inspired by Reifenberg's point of view, we introduce a model that combines the Ambrosio-Torterelli energy wit…
math.OC2025
Quantitative regularity properties for the optimal design problem
Lorenzo Lamberti, Antoine Lemenant
In this paper we slightly improve the regularity theory for the so called optimal design problem. We first establish the uniform rectifiability of the boundary of the optimal set,…