2017/02/14 by Nick Edelen, Edelen, Nick, Max Engelstein +1 · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1702.04325
openalex publication_date 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.