“A capillarity approach for the regularity of soap films”
Giovedì 14 Marzo 2024, ore 14:00 - Aula 2BC30 - Giulia Bevilacqua (Università di Pisa)
Abstract
We characterize boundary regularity for a variational model of soap film spanning a tubular neighborhood of a curve. Inspired by [1], soap films are chosen to be sets of finite perimeter containing a fixed volume and satisfying a topological spanning condition. In this talk, for a planar curve as midline of a tubular neighborhood, we show that minimizers are normal smooth graphs with constant mean curvature constructed over the plane and forming a contact angle equal to π/2 [2].
Joint work with Salvatore Stuvard (UNIMI) and Bozhidar Velichkov (UNIPI).
References
[1] D. King, F. Maggi, S. Stuvard, Plateau’s problem as a singular limit of capillarity problems, Communications on Pure and Applied Mathematics, 75:5 2022, pp. 895–969.
[2] G. Bevilacqua, S. Stuvard, B. Velichkov; Regularity of a free-boundary Plateau problem, in preparation.
