| Abstract: |
| In this talk, I will discuss the minimization problem of nematic liquid crystal droplets:
\begin{equation}
E(u,U)=1/2\int_U |Du|^2\,dx +\int_{\partial\Omega} f(u\cdot\nu) dH^{n-1}
\end{equation}
subject to $volume(U)=V_0>0$. The existence of minimization in a class of admissible domains, and some uniqueness (or rigidity) results in mean-convex, star-shaped domain will be presented. This is a joint work with Qinfeng Li (Hunan University, P.R.C). |
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