Calculus of Variations and Geometric Measure Theory

G. De Philippis - F. Maggi

Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law

created by maggi on 03 Feb 2014
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 3 feb 2014
Last Updated: 30 oct 2017

Journal: Arch. Ration. Mech. Anal.
Year: 2014

ArXiv: 1402.0549 PDF


Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed negligible set, showing in particular the validity of Young's law at almost every point of the free boundary. Our regularity results are not specific to capillarity problems, and actually apply to sets of finite perimeter (and thus to codimension one integer rectifiable currents) arising as minimizers in other variational problems with free boundaries.