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

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• 作者：Luc Nguyen (1)
  Arghir Zarnescu (2) (3)
  
• 关键词：35J60 ; 35Q56 ; 76A15 ; 58E20
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2013
• 出版时间：2 - May 2013
• 年：2013
• 卷：47
• 期：1
• 页码：383-432
• 全文大小：606KB
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• 作者单位：Luc Nguyen (1)
  Arghir Zarnescu (2) (3)
  
  1. Department of Mathematics, Princeton University, Princeton, NJ, USA
  2. OxPDE, Mathematical Institute, University of Oxford, Oxford, UK
  3. Department of Mathematics, University of Sussex, Brighton, UK
  
• ISSN：1432-0835

文摘

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 196:227-80, 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.