Journal article
On rank-one convex functions that are homogeneous of degree one
- Abstract:
- We show that positively $1$--homogeneous rank one convex functions are convex at $0$ and at matrices of rank one. The result is a special case of an abstract convexity result that we establish for positively $1$--homogeneous directionally convex functions defined on an open convex cone in a finite dimensional vector space. From these results we derive a number of consequences including various generalizations of the Ornstein $\LL^1$ non inequalities. Most of the results were announced in ({\em C.~R.~Acad.~Sci.~Paris, Ser.~I 349 (2011), 407--409}).
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Accepted manuscript, pdf, 196.8KB, Terms of use)
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- Publisher copy:
- 10.1007/s00205-016-0967-1
Authors
- Publisher:
- Springer Berlin Heidelberg
- Journal:
- Archive for Rational Mechanics and Analysis More from this journal
- Volume:
- 221
- Issue:
- 1
- Pages:
- 527-558
- Publication date:
- 2016-02-20
- Acceptance date:
- 2016-01-16
- DOI:
- EISSN:
-
1432-0673
- ISSN:
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0003-9527
- Keywords:
- Pubs id:
-
pubs:523440
- UUID:
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uuid:f01430e3-49c4-4aaf-86e9-c01fc9981aaa
- Local pid:
-
pubs:523440
- Source identifiers:
-
523440
- Deposit date:
-
2016-06-22
- ARK identifier:
Terms of use
- Copyright holder:
- Springer-Verlag Berlin Heidelberg
- Copyright date:
- 2016
- Notes:
-
This is an
accepted manuscript of a journal article published by Springer in Archive for Rational Mechanics and Analysis on 2016-02-20, available online: http://dx.doi.org/10.1007/s00205-016-0967-1
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