PreprintCC BY 4.0HAL
Uniform rectifiability of brittle fractures in linear elasticity
Abstract
We prove the uniform rectifiability of brittle fractures in arbitrary 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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BibTeX
@misc{labourie2026uniform,
title = {{Uniform rectifiability of brittle fractures in linear elasticity}},
author = {Camille Labourie},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05524464v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniform rectifiability of brittle fractures in linear elasticity
AU - Camille Labourie
PY - 2026
DA - 2026/09/18
PB - HAL
UR - https://hal.science/hal-05524464v2
AB - We prove the uniform rectifiability of brittle fractures in arbitrary 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''.
ER -