Preprint

Inserted: 21 jul 2026
Last Updated: 21 jul 2026

Year: 2026

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 $SBV^2$.

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