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arXiv · 1407.4834

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

Guido De Philippis·Francesco Maggi
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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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Guido De Philippis, Francesco Maggi. 2014-07-17. Dimensional estimates for singular sets in geometric variational problems with free boundaries. https://arxiv.org/abs/1407.4834

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