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On approximate differentiability of functions with bounded deformation

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Abstract

We prove that functions with bounded deformationu: Ω → ℝn, Ω ⊂ ℝn, i.e., such mappings that the symmetric part of the gradient\(\frac{1}{2}\left( {\nabla u + \left( {\nabla u} \right)^T } \right)\) is a measure, are approximately differentiable a.e. Then we generalize the result to a more general class of functions.

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Authors and Affiliations

  1. Institute on Mathematics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Piotr Hajłasz

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  1. Piotr Hajłasz
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This research was carried out while the author stayed in the ICTP in Trieste in 1995. He wishes to thank the ICTP for the hospitality. The author was partially supported by KBN grant no. 2-PO3A-034-08.

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Hajłasz, P. On approximate differentiability of functions with bounded deformation. Manuscripta Math 91, 61–72 (1996). https://doi.org/10.1007/BF02567939

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  • DOI: https://doi.org/10.1007/BF02567939

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