Geodesic
Generalised functions of bounded deformation
Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1943-1997

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We introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD 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.
DOI : 10.4171/jems/410
Classification : 49-XX, 26-XX, 46-XX, 00-XX
Keywords: free discontinuity problems, special functions of bounded deformation, jump set, rectifiability, slicing, approximate differentiability 
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     author = {Gianni Dal Maso},
     title = {Generalised functions of bounded deformation},
     journal = {Journal of the European Mathematical Society},
     pages = {1943--1997},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2013},
     doi = {10.4171/jems/410},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/410/}
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Gianni Dal Maso. Generalised functions of bounded deformation. Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1943-1997. doi: 10.4171/jems/410

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