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math.OC2025
Optimal regularity up to the boundary for Plateau-quasi-minimizers
Eve Machefert
We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-…
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…