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arXiv · 1003.2470

Regularity for non-local almost minimal boundaries and applications

M. Cristina Caputo·Nestor Guillen
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Abstract

We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal boundaries are smooth. This can be viewed as a non-local version of the Almgren-De Giorgi-Tamanini regularity theory. The main result has several applications, among these $C^{1,α}$ regularity for sets with prescribed non-local mean curvature in $L^p$ and regularity of solutions to non-local obstacle problems.

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M. Cristina Caputo, Nestor Guillen. 2011-06-09. Regularity for non-local almost minimal boundaries and applications. https://arxiv.org/abs/1003.2470

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