Analysis Seminar

A capillarity approach for the regularity of soap films

by Giulia Bevilacqua (Università di Pisa)

Sala Riunioni (Dipartimento di Matematica )

Sala Riunioni

Dipartimento di Matematica


We characterize boundary regularity for a specific variational soap film model. 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 [2], for a planar curve as the midline of the tubular neighborhood, we show that minimizers are normal smooth graphs with constant mean curvature constructed over the plane and forming on the tubular neighborhood a contact angle equal to $\pi/2$.

Joint work with Salvatore Stuvard (UNIMI) and Bozhidar Velichkov (UNIPI).

[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.