Calculus of Variations and Geometric Measure Theory

D. King - F. Maggi - S. Stuvard

Plateau's problem as a singular limit of capillarity problems

created by stuvard on 01 Jul 2019
modified on 24 Mar 2022


Published Paper

Inserted: 1 jul 2019
Last Updated: 24 mar 2022

Journal: Comm. Pure Appl. Math.
Volume: 75
Number: 5
Pages: 895-969
Year: 2022
Doi: 10.1002/cpa.22048

ArXiv: 1907.00551 PDF
Links: CPAM


Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions.

Keywords: minimal surfaces, Plateau's problem, Capillarity theory