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Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands

Abstract:
We consider the class of non-negative rank-one convex isotropic integrands on Rn×n which are also positively p-homogeneous. If p≤n=2 we prove, conditional on the quasiconvexity of the Burkholder integrand, that the integrands in this class are quasiconvex at conformal matrices. If p≥n=2, we show that the positive part of the Burkholder integrand is polyconvex. In general, for p≥n, we prove that the integrands in the above class are polyconvex at conformal matrices. Several examples imply that our results are all nearly optimal.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00205-022-01792-2

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
ORCID:
0000-0002-8302-5953
Publisher:
Springer
Journal:
Archive for Rational Mechanics and Analysis More from this journal
Volume:
245
Pages:
479-500
Publication date:
2022-05-22
Acceptance date:
2022-04-25
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
Language:
English
Keywords:
Pubs id:
1251488
Local pid:
pubs:1251488
Deposit date:
2022-04-23

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