Minimizers of a variational problem for nematic liquid crystals with variable degree of orientation in two dimensions

Abstract: We study the asymptotic behavior, when k→∞, of the minimizers of the energy Gk(u)=∫_Ω((k−1)|(∇|u|)|^2+|∇u|^2), over the class of maps u∈H^1(Ω, R2) satisfying the boundary condition u=g on ∂Ω, where Ω is a smooth, bounded and simply connected domain in R^2 and g:∂Ω→S^1. The motivation comes from a simplified version of Ericksen model for nematic liquid crystals. We will present similarities and differences with respect to the analog problem for the Ginzburg-Landau energy.

Based on a joint work with Dmitry Golovaty.

analysis of PDEsdynamical systemsfunctional analysisoptimization and controlspectral theory

Audience: advanced learners

Webinar on PDE and related areas

Series comments: The webinar is organised jointly from IIT-Kanpur, TIFR-CAM,Bangalore, IISER-Pune and IISER-Kolkata.

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