Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - A. Coscia - G. Dal Maso

Fine Properties of Functions with Bounded Deformation

created on 01 Apr 1996
modified on 28 Jun 2001


Published Paper

Inserted: 1 apr 1996
Last Updated: 28 jun 2001

Journal: Arch. Rational Mech. Anal.
Volume: 139
Pages: 201-238
Year: 1997


The paper is concerned with the fine properties of functions u in BD, 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 BV, 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 BD functions, showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections. Moreover, we prove that BD functions are approximately differentiable in almost every point of their domain.


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