Compactness and lower semicontinuity in GSBD

2018/02/08 by Chambolle, Antonin, Crismale, Vito · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.03302

Abstract

In this paper, we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in (G)SBV by Ambrosio and SBD by Bellettini-Coscia-Dal Maso. As a result, the static problem in Francfort-Marigo's variational approach to crack growth admits (weak) solutions. Moreover, we obtain a compactness property for minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have recently shown the Γ-convergence to Griffith energy.

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• Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane

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