Compactness and lower semicontinuity in

  • Antonin Chambolle

    École Polytechnique, Palaiseau, France
  • Vito Crismale

    École Polytechnique, Palaiseau, France
Compactness and lower semicontinuity in $GSBD$ cover
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Abstract

In this paper we prove a compactness and semicontinuity result in for sequences with bounded Griffith energy. This generalises classical results in () by Ambrosio [1, 2, 4] and SBD by Bellettini–Coscia–Dal Maso [9]. As a result, the static problem in Francfort–Marigo’s variational approach to crack growth [30] admits (weak) solutions.

Cite this article

Antonin Chambolle, Vito Crismale, Compactness and lower semicontinuity in . J. Eur. Math. Soc. 23 (2021), no. 3, pp. 701–719

DOI 10.4171/JEMS/1021