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

Generalised functions of bounded deformation

  • Gianni Dal Maso

    SISSA, Trieste, Italy
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Abstract

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.

Cite this article

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

DOI 10.4171/JEMS/410