Shape Sensitivity for a Class of Liquid Crystal Models

Luis González-Valencia () and Rajesh Mahadevan ()
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Luis González-Valencia: Facultad de Ciencias, Universidad Austral de Chile
Rajesh Mahadevan: Universidad de Concepción

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 17, 24 pages

Abstract: Abstract In this article we obtain a shape sensitivity result for the equilibrium energy, in the Oseen-Frank model, of a nematic liquid crystal under normal anchoring. As an application we show that, for a nematic liquid crystal confined between two parallel cylindrical domains, the coaxial configuration is a critical state for the equilibrium energy. The application partially solves a conjecture made by Alouges and Coleman (Math Models Methods Appl Sci 11:459–473, 2001) based on numerical evidence.

Keywords: Liquid crystal; Oseen-Frank model; Shape semi-derivative; Optimisation; 76A15; 46A15; 49Q10; 82D30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02614-7

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