Compactness and lower semicontinuity in $GSBD$

@article{Chambolle2018CompactnessAL,
  title={Compactness and lower semicontinuity in \$GSBD\$},
  author={A. Chambolle and V. Crismale},
  journal={arXiv: Functional Analysis},
  year={2018}
}
  • A. Chambolle, V. Crismale
  • Published 2018
  • Mathematics
  • arXiv: Functional Analysis
  • 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 $\Gamma$-convergence… CONTINUE READING
    23 Citations
    Non-local approximation of the Griffith functional

    References

    SHOWING 1-10 OF 37 REFERENCES
    Korn-Poincaré inequalities for functions with a small jump set
    • 31
    • PDF
    A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results
    • 21
    • PDF
    Generalised functions of bounded deformation
    • 59
    • Highly Influential
    • PDF
    Lower Semicontinuity Properties of Functionals with Free Discontinuities
    • 21
    Existence and convergence for quasi-static evolution in brittle fracture
    • 174
    Piecewise rigidity
    • 34
    • PDF
    Quasistatic crack growth in 2d-linearized elasticity
    • 25
    • PDF
    Traces of functions of bounded deformation
    • 34
    • PDF