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 / Guido De Philippis; Francesco Maggi. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - STAMPA. - 0:(2017), pp. 217-234. [10.1515/crelle-2014-0100]
Dimensional estimates for singular sets in geometric variational problems with free boundaries
MAGGI, FRANCESCO
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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