Abstract
The paper is concerned with the fine properties of functions in , the space of functions with bounded deformation. We analyse the set of Lebesgue points and the set where these functions have one-sided approximate limits. Moreover, following the analogy with , we decompose the symmetric distributional derivative into an absolutely continuous part , a jump part , and a Cantor part . The main result of the paper is a structure theorem for functions, showing that these parts of the derivative can be recovered from the corresponding ones of the one-dimensional sections. Moreover, we prove that functions are approximately differentiable in almost every point of their domain.
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(Accepted March 19, 1996)
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Ambrosio, L., Coscia, A. & Maso, G. Fine Properties of Functions with Bounded Deformation. Arch Rational Mech Anal 139, 201–238 (1997). https://doi.org/10.1007/s002050050051
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DOI: https://doi.org/10.1007/s002050050051