3 papers
math.AP2026
Existence and Regularity of Minimizers for a Plateau Approximation Problem
Eve Machefert
In this paper, we study the functional introduced by the author in collaboration with Bonnivard, Bretin, and Lemenant, which is designed to approximate Plateau's problem. We establ…
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…