Work

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

Year: 2023

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2310.07670

Authors: Friedrich, Manuel, Labourie, Camille, Stinson, Kerrek

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1652504919, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur, G591746060, G6938060324, G7207901211

OpenAlex ID: W4387596592

Cites:

Cited by:

Related to: 10