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arXiv · 1702.04325

Quantitative stratification for some free-boundary problems

Nick Edelen·Max Engelstein
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Abstract

In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli. Our main tools are the Quantitative Stratification and Rectifiable-Reifenberg framework of Naber-Valtorta, which allow us to do a type of "effective dimension-reduction." The arguments are sufficiently robust that they apply to a broad class of related free boundary problems as well.

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Nick Edelen, Max Engelstein. 2017-02-14. Quantitative stratification for some free-boundary problems. https://arxiv.org/abs/1702.04325

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