Quantitative stratification for some free-boundary problems

  title={Quantitative stratification for some free-boundary problems},
  author={Nick Edelen and Max Engelstein},
  journal={Transactions of the American Mathematical Society},
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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