An epsilon-regularity result for Griffith almost-minimizers in the plane

2023/10/11 by Friedrich, Manuel, Labourie, Camille, Stinson, Kerrek · 1 citation
#49J45 #70G75 #74A30 #74B20 #74G65 #74R10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.07670

Abstract

We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity theorem showing that the crack is locally a C^1,1/2 curve outside of a singular set of zero Hausdorff measure. The main novelty is that, in contrast to previous results, no topological constraints on the crack are required. The results also apply to almost-minimizers.

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• Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane

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