Existence and Regularity of Minimizers for a Plateau Approximation Problem
Abstract
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 establish the existence of a minimizer and prove its H{ö}lder regularity. Our results may be viewed as a generalization to higher-dimensional surfaces of the one-dimensional work of Bonnivard, Lemenant, and Millot on the approximation of the Steiner problem.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Numerical Methods in Computational Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint