We study generalized minimizers in the soap film capillarity model introduced in King et al. (Commun Pure Appl Math, 2020. https://doi.org/10.1002/cpa.21951) and Maggi et al. (Discrete Contin Dyn Syst 39(12):6877–6912, 2019). Collapsed regions of generalized minimizers are shown to be smooth outside of dimensionally small singular sets, which are thus empty in physical dimensions. Since generalized minimizers converge to Plateau’s type surfaces in the vanishing volume limit, the fact that collapsed regions cannot exhibit Y -points and T -points (which are possibly present in the limit Plateau’s surfaces) gives the first strong indication that singularities of the limit Plateau’s surfaces should always be “wetted” by the bulky regions of the approximating generalized minimizers.

Smoothness of collapsed regions in a capillarity model for soap films / D. King, F. Maggi, S. Stuvard. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 243:2(2022 Feb), pp. 459-500. [10.1007/s00205-021-01727-3]

Smoothness of collapsed regions in a capillarity model for soap films

S. Stuvard
Ultimo
2022-02

Abstract

We study generalized minimizers in the soap film capillarity model introduced in King et al. (Commun Pure Appl Math, 2020. https://doi.org/10.1002/cpa.21951) and Maggi et al. (Discrete Contin Dyn Syst 39(12):6877–6912, 2019). Collapsed regions of generalized minimizers are shown to be smooth outside of dimensionally small singular sets, which are thus empty in physical dimensions. Since generalized minimizers converge to Plateau’s type surfaces in the vanishing volume limit, the fact that collapsed regions cannot exhibit Y -points and T -points (which are possibly present in the limit Plateau’s surfaces) gives the first strong indication that singularities of the limit Plateau’s surfaces should always be “wetted” by the bulky regions of the approximating generalized minimizers.
soap films; minimal surfaces; regularity theory
Settore MAT/05 - Analisi Matematica
6-gen-2022
https://link.springer.com/article/10.1007/s00205-021-01727-3
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850447
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