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Refined approximation for minimizers of a Landau-de Gennes energy functional

Abstract:
We study minimizers of a Landau-de Gennes energy functional in the asymptotic regime of small dimensionless elastic constant L > 0. The results on the convergence to a minimizer of the limit Oseen-Frank functional in Majumdar and Zarnescu (Arch Ration Mech Anal 196:227–280, 2010) are revisited and improved, which in effect lead to a sharp rate of convergence. The equation for the first-order correction term is derived: it has a “normal component” given by an algebraic relation and a “tangential component” given by a linear system.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00526-012-0522-3

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Author
Publisher:
Springer Publisher's website
Journal:
Calculus of Variations and Partial Differential Equations Journal website
Volume:
47
Issue:
1-2
Pages:
383–432
Publication date:
2012-04-17
Acceptance date:
2012-03-10
DOI:
EISSN:
1432-0835
ISSN:
0944-2669
Source identifiers:
146862
Keywords:
Pubs id:
pubs:146862
UUID:
uuid:44de260b-4255-4644-8b0a-be791971095c
Local pid:
pubs:146862
Deposit date:
2018-06-21

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