Quantitative stratification for some free-boundary problems

Nick Edelen, M. A.X. Engelstein

Research output: Contribution to journalArticle

4 Scopus citations


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 [J. Reine Angew. Math. 325 (1981), pp. 105–144]. Our main tools are the Quantitative Stratification and Rectifiable-Reifenberg framework of Naber–Valtorta [Ann. of Math. (2) 185 (2017), pp. 131–227], 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.

Original languageEnglish (US)
Pages (from-to)2043-2072
Number of pages30
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - Jan 1 2019
Externally publishedYes

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