JournalsjemsVol. 15, No. 5pp. 1943–1997

Generalised functions of bounded deformation

  • Gianni Dal Maso

    SISSA, Trieste, Italy
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We introduce the space GBDGBD of generalized functions of bounded deformation and study the structure properties of these functions: the recti ability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBDGBD, which leads to a compactness result for the space GSBDGSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

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Gianni Dal Maso, Generalised functions of bounded deformation. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1943–1997

DOI 10.4171/JEMS/410