caa a22 4500 605515115 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s00205-014-0813-2 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0813-2 Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young's Law [Elektronische Daten] [G. Philippis, F. Maggi] 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. Springer-Verlag Berlin Heidelberg, 2014 Philippis G. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany aut Maggi F. Department of Mathematics, The University of Texas at Austin, 2515 Speedway Stop C1200, 78712-1202, Austin, TX, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/2(2015-05-01), 473-568 0003-9527 216:2<473 2015 216 205 https://doi.org/10.1007/s00205-014-0813-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0813-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Philippis G. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany aut NATIONALLICENCE 700 1- Maggi F. Department of Mathematics, The University of Texas at Austin, 2515 Speedway Stop C1200, 78712-1202, Austin, TX, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/2(2015-05-01), 473-568 0003-9527 216:2<473 2015 216 205