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Characterization of generalized young measures generated by symmetric gradients
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de Philippis, Guido and Rindler, Filip (2017) Characterization of generalized young measures generated by symmetric gradients. Archive for Rational Mechanics and Analysis, 224 (3). pp. 1087-1125. doi:10.1007/s00205-017-1096-1 ISSN 0003-9527.
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Official URL: http://doi.org/10.1007/s00205-017-1096-1
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.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Asymptotic theory, Calculus of variations | ||||||||
| Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0003-9527 | ||||||||
| Official Date: | June 2017 | ||||||||
| Dates: |
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| Volume: | 224 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 1087-1125 | ||||||||
| DOI: | 10.1007/s00205-017-1096-1 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 2 March 2017 | ||||||||
| Date of first compliant Open Access: | 2 March 2017 | ||||||||
| Funder: | Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | RBSI14RVEZ (MIUR), EP/L018934/1 (EPSRC) |
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