Calculus of Variations and Geometric Measure Theory

G. De Philippis - F. Rindler

Characterization of generalized Young measures generated by symmetric gradients

created by dephilipp on 14 Apr 2016
modified on 30 Oct 2017


Accepted Paper

Inserted: 14 apr 2016
Last Updated: 30 oct 2017

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

ArXiv: 1604.04097 PDF


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.