Refined approximation for minimizers of a Landau-de Gennes energy functional |
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Authors: | Luc Nguyen Arghir Zarnescu |
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Institution: | 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
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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. |
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