Characterization of Young measures generated by sequences in BV an BD

Details Characterization of Young measures generated by sequences in BV an BD Characterization of Young measures generated by sequences in BV an BD

2011-12-23

arxiv.org/abs/1112.5613v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

First, this work presents a new and improved proof strategy for the recent characterization theorem for generalized Young measures generated by sequences in BV by Kristensen and the author [Arch. Ration. Mech. Anal. 197 (2010), 539-598]. The present proof is based on a localization technique together with a rigidity argument and avoids employing a relaxation theorem. Then, based on this new technique, we prove an analogous characterization result for Young measures generated by sequences in the space BD of functions of bounded deformation. This theorem places these Young measures in duality to symmetric-quasiconvex functions. For this purpose we need to strengthen a recent rigidity result for BD-functions and their associated tangent Young measures, which is also interesting in its own right. Finally, as an application of the characterization theorem, we show how for Young measures with an "atomic" part one can find a generating sequence respecting this structure.

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