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

G. De Philippis, F. Maggi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)473-568
Number of pages96
JournalArchive for Rational Mechanics and Analysis
Volume216
Issue number2
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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