Quantitative stratification for some free-boundary problems
Analysis of PDEs
2017-09-19 v3
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.
Keywords
Cite
@article{arxiv.1702.04325,
title = {Quantitative stratification for some free-boundary problems},
author = {Nick Edelen and Max Engelstein},
journal= {arXiv preprint arXiv:1702.04325},
year = {2017}
}
Comments
This version has minor corrections and additional references