The two-dimensional liquid crystal droplet problem with a tangential boundary condition

DOI10.1007/S00205-021-01733-5zbMath1487.76007arXiv2106.10668OpenAlexW4205878347MaRDI QIDQ2113535

Zhiyuan Geng, Fang-Hua Lin

Publication date: 14 March 2022

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.10668

zbMATH Keywords

Sobolev spaceexistencefree boundary problemshape optimizationlarge volume asymptotic solutionOseen-Frank energy functionalWeil-Peterssen curve class

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Variational methods applied to problems in fluid mechanics (76M30) Liquid crystals (76A15) Liquid-gas two-phase flows, bubbly flows (76T10)

Cites Work

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• The boundary correspondence under quasiconformal mappings
• Liquid crystals with variable degree of orientation
• Rectifiable sets and the traveling salesman problem
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• Drops of nematic liquid crystals
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• Lifting in Sobolev spaces
• Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces
• Axisymmetric configurations of bipolar liquid crystal droplets
• A model problem for nematic-isotropic transitions with highly disparate elastic constants
• A coupled Ericksen/Allen-Cahn model for liquid crystal droplets
• The sharp quantitative isoperimetric inequality
• Quasiconformal reflections
• Two transitions in tangentially anchored nematic droplets
• Injectivity theorems in plane and space
• Hardy spaces, $A_\infty$, and singular integrals on chord-arc domains
• Weil-Petersson metric on the universal Teichmüller space
• Ginzburg-Landau vortices

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