Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young’s Law

By Guido De Philippis, Francesco Maggi. Archive for Rational Mechanics and Analysis, 2014

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/021abdc60258e53f8031d86f27b0435e7c86f1c9