Smoothness of Collapsed Regions in a Capillarity Model for Soap Films

King, Darren; Maggi, Francesco; Stuvard, Salvatore

doi:10.1007/s00205-021-01727-3

Arch Rational Mech Anal

2022

DOI: 10.1007/s00205-021-01727-3

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Smoothness of Collapsed Regions in a Capillarity Model for Soap Films

Darren King

Francesco Maggi

Salvatore Stuvard

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2024

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Cited by 1 publication

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On the Relaxation of Gauss’s Capillarity Theory Under Spanning Conditions

Novack

2024

J Geom Anal

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We study a variational model for soap films in which the films are represented by sets with fixed small volume rather than surfaces. In this problem, a minimizing sequence of completely “wet" films, or sets of finite perimeter spanning a wire frame, may converge to a film containing both wet regions of positive volume and collapsed (dry) surfaces. When collapsing occurs, these limiting objects lie outside the original minimization class and instead are admissible for a relaxed problem. Here we show that the relaxation and the original formulation are equivalent by approximating the collapsed films in the relaxed class by wet films in the original class.

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On the Relaxation of Gauss’s Capillarity Theory Under Spanning Conditions

Novack

2024

J Geom Anal

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Smoothness of Collapsed Regions in a Capillarity Model for Soap Films

Cited by 1 publication

References 24 publications

On the Relaxation of Gauss’s Capillarity Theory Under Spanning Conditions

On the Relaxation of Gauss’s Capillarity Theory Under Spanning Conditions

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