Fulltext

Dimensional estimates for singular sets in geometric variational problems with free boundaries

De Philippis, Guido ; Maggi, Francesco

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2017, vol. 2017, no. 725, p. 217-234

Add to personal list
    Title
    • Dimensional estimates for singular sets in geometric variational problems with free boundaries
    Author
    • De Philippis, Guido. Institut für Mathematik, Universität Zürich,CH-8057 Zürich, Switzerland
    • Maggi, Francesco. Department of Mathematics, The University of Texas at Austin, 2515 Speedway Stop C1200, Austin, Texas 78712-1202, USA
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Journal für die reine und angewandte Mathematik (Crelles Journal), 2017, vol. 2017, no. 725, p. 217-234. De Gruyter
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:332417
    Summary
    We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are ℋ n - 3 ${\mathcal{H}^{n-3}}$ -negligible, where n is the ambient space dimension. In particular our results apply to capillarity type problems, and establish everywhere regularity in the three-dimensional case.