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.

Plateau's Problem as a Singular Limit of Capillarity Problems / D. King, F. Maggi, S. Stuvard. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 75:3(2022), pp. 541-609. [10.1002/cpa.22019]

Plateau's Problem as a Singular Limit of Capillarity Problems

S. Stuvard
2022

Abstract

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.
Settore MAT/05 - Analisi Matematica
30-ago-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/870034
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