Quantitative stratification for some free-boundary problems

Nick Edelen, M. A.X. Engelstein

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 [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
Volume371
Issue number3
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Funding Information:
Received by the editors February 24, 2017, and, in revised form, September 12, 2017. 2010 Mathematics Subject Classification. Primary 35R35. The first author was supported by NSF grant DMS-1606492. The second author was partially supported by NSF Grant No. DMS-1440140 while the author was in residence at MSRI in Berkeley, California, during Spring 2017.

Publisher Copyright:
© 2018 American Mathematical Society.

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