Calculus of Variations and Geometric Measure Theory
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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 29 Jul 2014

[BibTeX]

Accepted Paper

Inserted: 17 jul 2014
Last Updated: 29 jul 2014

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

Abstract:

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.


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