Date/heure
5 mai 2026
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Eve MACHEFERT
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
Plateau’s problem is a notorious problem in Calculus of Variations and Geometric Measure Theory. In this presentation, I will introduce a phase-field approximation of Plateau’s problem, based on the coupling of the Ambrosio–Tortorelli energy with a geodesic distance penalization, which encodes the topological constraints. I will then justify this approach through a Γ-convergence result towards a formulation of Plateau’s problem in codimension one, and analyze the functional by establishing existence and regularity results for minimizers. From an analytical perspective, I will also present an analysis of the limit problem and provide a characterization of quasi-minimizers in terms of John domains. Finally, this approach is implemented in a numerical framework to approximate solutions of Plateau’s problem in various configurations, illustrating the efficiency and flexibility of the proposed model.