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<p>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.</p>

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Shape Sensitivity for a Class of Liquid Crystal Models

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Luis González-Valencia,
  • Rajesh Mahadevan

摘要

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.