Calculus of Variations and Geometric Measure Theory
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G. De Philippis - F. Rindler

Characterization of generalized Young measures generated by symmetric gradients

created by dephilipp on 14 Apr 2016
modified on 28 Jan 2017


Accepted Paper

Inserted: 14 apr 2016
Last Updated: 28 jan 2017

Journal: Arch. Ration. Mech. An.
Year: 2016


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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