Characterization of Generalized Young Measures Generated by Symmetric Gradients

Guido De Philippis, Filip Rindler

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1087-1125
Number of pages39
JournalArchive for Rational Mechanics and Analysis
Volume224
Issue number3
DOIs
StatePublished - Jun 1 2017

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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