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

Guido De Philippis; Francesco Maggi

doi:10.1515/crelle-2014-0100

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

Guido De Philippis, Francesco Maggi

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	217-234
Number of pages	18
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2017
Issue number	724
DOIs	https://doi.org/10.1515/crelle-2014-0100
State	Published - Apr 2017

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/crelle-2014-0100

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title = "Dimensional estimates for singular sets in geometric variational problems with free boundaries",

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.",

author = "{De Philippis}, Guido and Francesco Maggi",

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AU - Maggi, Francesco

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

Abstract

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