Calculus of Variations and Geometric Measure Theory

C. Labourie

Uniform rectifiability of brittle fractures in linear elasticity

created by labourie on 27 Feb 2026

[BibTeX]

Preprint

Inserted: 27 feb 2026
Last Updated: 27 feb 2026

Year: 2026

Abstract:

We prove the uniform rectifiability of brittle fractures in abritrary dimension. The existing approach for the Mumford-Shah functional, which relies on separation-type properties of the singular set, faces serious obstacles in the Griffith setting due to the lack of coarea formula for the symmetric gradient. We present an alternative route to uniform rectifiability for free-discontinuity problems by proving that cracks have "plenty of big projections".


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