In this note we prove an abstract version of a recent quantitative stratification principle introduced by Cheeger and Naber (2013) [6] and [7]. Using this general regularity result paired with an ε-regularity theorem we provide a new estimate of the Minkowski dimension of the set of higher multiplicity points of a Dir-minimizing Q-valued function. The abstract principle is applicable to several other problems: we recover recent results in the literature and we obtain also some improvements in more classical contexts.
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result / Matteo, Focardi; Andrea, Marchese; Emanuele Nunzio, Spadaro. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 268:(2015), pp. 3290-3325. [10.1016/j.jfa.2015.02.011]
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result
FOCARDI, MATTEO;
2015
Abstract
In this note we prove an abstract version of a recent quantitative stratification principle introduced by Cheeger and Naber (2013) [6] and [7]. Using this general regularity result paired with an ε-regularity theorem we provide a new estimate of the Minkowski dimension of the set of higher multiplicity points of a Dir-minimizing Q-valued function. The abstract principle is applicable to several other problems: we recover recent results in the literature and we obtain also some improvements in more classical contexts.File | Dimensione | Formato | |
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