Epsilon-Regularity for Griffith Almost-Minimizers in Any Dimension Under a Separating Condition

Labourie C, Lemenant A (2023)


Publication Type: Journal article

Publication year: 2023

Journal

Book Volume: 247

Article Number: 105

Journal Issue: 6

DOI: 10.1007/s00205-023-01935-z

Abstract

In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is ε -close to a plane in some ball B⊂ RN while separating the ball B in two big parts, then K is C1,α in a slightly smaller ball. Our result contains and generalizes the 2 dimensional result of Babadjian et al. (J Eur Math Soc 24(7):2443–2492, 2022), with a different and more sophisticate approach inspired by Lemenant (Ann Sc Norm Super Pisa Cl Sci 9(2):351–384, 2010; Ann Sc Norm Super Pisa Cl Sci 10(3):561–609, 2011), using also Labourie (J Geom Anal 31(10):10024–10135, 2021) in order to adapt a part of the argument to Griffith minimizers.

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APA:

Labourie, C., & Lemenant, A. (2023). Epsilon-Regularity for Griffith Almost-Minimizers in Any Dimension Under a Separating Condition. Archive for Rational Mechanics and Analysis, 247(6). https://doi.org/10.1007/s00205-023-01935-z

MLA:

Labourie, Camille, and Antoine Lemenant. "Epsilon-Regularity for Griffith Almost-Minimizers in Any Dimension Under a Separating Condition." Archive for Rational Mechanics and Analysis 247.6 (2023).

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