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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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Publisher copy:
10.1007/s00205-016-0967-1

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author


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:
0003-9527


Keywords:
Pubs id:
pubs:523440
UUID:
uuid:f01430e3-49c4-4aaf-86e9-c01fc9981aaa
Local pid:
pubs:523440
Source identifiers:
523440
Deposit date:
2016-06-22
ARK identifier:

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