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.

Characterization of Generalized Young Measures Generated by Symmetric Gradients / De Philippis, Guido; Rindler, Filip. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 224:3(2017), pp. 1087-1125. [10.1007/s00205-017-1096-1]

Characterization of Generalized Young Measures Generated by Symmetric Gradients

De Philippis, Guido;
2017-01-01

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.
2017
224
3
1087
1125
http://link.springer-ny.com/link/service/journals/00205/index.htm
https://arxiv.org/abs/1604.04097
De Philippis, Guido; Rindler, Filip
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/60726
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