Calculus of Variations and Geometric Measure Theory

D. King - F. Maggi - S. Stuvard

Smoothness of collapsed regions in a capillarity model for soap films

created by maggi on 29 Jul 2020
modified by stuvard on 04 Feb 2022


Published Paper

Inserted: 29 jul 2020
Last Updated: 4 feb 2022

Journal: Arch. Ration. Mech. Anal.
Volume: 243
Number: 2
Pages: 459-500
Year: 2022
Doi: 10.1007/s00205-021-01727-3

ArXiv: 2007.14868 PDF
Links: ARMA


We study generalized minimizers in the soap film capillarity model introduced in arXiv:1807.05200 and arXiv:1907.00551. 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.