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Archive for Rational Mechanics and Analysis

, Volume 224, Issue 3, pp 1087–1125 | Cite as

Characterization of Generalized Young Measures Generated by Symmetric Gradients

  • Guido De Philippis
  • Filip Rindler
Open Access
Article

Abstract

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer–Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The “local” proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti’s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.SISSATriesteItaly
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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