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

Abstract: We study the asymptotic behavior,  when $k\to\infty$, of the minimizers of the energy 
\begin{equation*}
G_k(u)=\int_{\Omega}\Big((k-1)|
abla|u||^2+|
abla 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.