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A local proof for the characterization of Young measures generated by sequences in BV
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Rindler, Filip (2014) A local proof for the characterization of Young measures generated by sequences in BV. Journal of Functional Analysis, Volume 266 (Number 11). pp. 6335-6371. doi:10.1016/j.jfa.2014.03.010 ISSN 0022-1236.
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Official URL: http://dx.doi.org/10.1016/j.jfa.2014.03.010
Abstract
This work presents a new proof of the recent characterization theorem for generalized Young measures generated by sequences in BV by Kristensen and Rindler (2010) [14]. The present argument is based on a localization technique together with a local Hahn–Banach argument in novel function spaces combined with an application of Alberti's Rank-One Theorem. This strategy avoids employing a relaxation theorem as in the previously known proof, and the new tools introduced in its course should prove useful in other contexts as well. In particular, we introduce “homogeneous” Young measures, separately at regular and singular points, which exhibit rather different behavior than the classical homogeneous Young measures. As an application, we show how for BV-Young measures with an “atomic” part one can find a generating sequence respecting this structure.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Functions of bounded variation | ||||||||
| Journal or Publication Title: | Journal of Functional Analysis | ||||||||
| Publisher: | Academic Press | ||||||||
| ISSN: | 0022-1236 | ||||||||
| Official Date: | June 2014 | ||||||||
| Dates: |
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| Volume: | Volume 266 | ||||||||
| Number: | Number 11 | ||||||||
| Page Range: | pp. 6335-6371 | ||||||||
| DOI: | 10.1016/j.jfa.2014.03.010 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 28 December 2015 | ||||||||
| Date of first compliant Open Access: | 28 December 2015 |
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