Preprint

Inserted: 30 jun 2025
Last Updated: 30 jun 2025

Year: 2025

Abstract:

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 with a geodesic distance term which can be considered as a generalization of the approach developed in LS14, BLS15 to approximate solutions to the Steiner problem. First, we present a Γ-convergence analysis of this model in the simple case of a single curve located on the edge of a cylinder. In a numerical section, we detail the numerical optimisation schemes used to minimize this energy for numerous examples, for which good approximation of solutions to Plateau’s problem are found.

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• Gamm_conv_Plateau.pdf