Good access to the crack and integrability of the full gradient for Griffith almost-minimizers in the plane

2026/07/21 by Camille Labourie, Lorenzo Lamberti, Antoine Lemenant
#math.AP

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Abstract

We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement satisfies Hölder-type estimates. As a consequence, we derive the integrability of the full gradient and the finiteness of the traces along the crack. In particular, we show that any Griffith almost-minimizer in dimension two locally belongs to the space SBV².

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