FALL 2021 Nonlinear Analysis Seminar Series

Professor Itai Shafrir,  Technion-Israel Institute of Technology

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

We study the asymptotic behavior, when $k \to \infty$, of the minimizers of the energy $$\begin{equation*} G_k(u)=\int_{\Omega}\Big((k-1)|\nabla|u||^2+|\nabla u|^2\Big)\,, \end{equation*}$$ over the class of maps $u\in H^1(\Omega,{\mathbb R}^2)$ satisfying the boundary condition $u=g$ on $\partial\Omega$, where $\Omega$ is a smooth, bounded and simply connected domain in ${\mathbb R}^2$ and $g:\partial\Omega\to S^1$. 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.

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