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Generalised functions of bounded deformation

TitleGeneralised functions of bounded deformation
Publication TypeJournal Article
Year of Publication2011
AuthorsDal Maso, G
JournalJ. Eur. Math. Soc. (JEMS), to appear
Keywordsfree discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability

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.


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