Calculus of Variations and Geometric Measure Theory

G. De Philippis - F. Maggi

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

created by maggi on 17 Jul 2014
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 17 jul 2014
Last Updated: 30 oct 2017

Journal: J. Reine Angew. Math.
Pages: 15
Year: 2014

ArXiv: 1407.4834 PDF


We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are $\mathcal H ^{n-3}$-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.