We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are Hn-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.
Dimensional estimates for singular sets in geometric variational problems with free boundaries
De Philippis G.;
2017
Abstract
We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are Hn-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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