Improved estimate of the singular set of Dir-minimizing Q-valued\n functions via an abstract regularity result

2014/09/08 by Matteo Focardi, Focardi, Matteo, Andrea Marchese +3
Computer Science · Mathematics · #49Q20 #54E40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1409.2320

openalex publication_date 2014/09/08 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In this note we prove an abstract version of a recent quantitative\nstratifcation priciple introduced by Cheeger and Naber (Invent. Math., 191\n(2013), no. 2, 321-339; Comm. Pure Appl. Math., 66 (2013), no. 6, 965-990).\nUsing this general regularity result paired with an \ε-regularity\ntheorem we provide a new estimate of the Minkowski dimension of the set of\nhigher multiplicity points of a Dir-minimizing Q-valued function. The abstract\npriciple is applicable to several other problems: we recover recent results in\nthe literature and we obtain also some improvements in more classical contexts.\n

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