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学术报告十一:A minimizing problem involving nematic liquid crystal droplets

来源:数学与统计学院     作者:     时间:2017/6/5 11:35:13  0次

数学与统计院学术报告[2017] 011

(高水平大学建设系列报告081)

讲座题目: A minimizing problem involving nematic liquid crystal droplets.

讲座人:Changyou Wang (Purdue University, USA) 

讲座时间:6月6日 下午3:00-400

讲座地点:科技楼514                                 

报告内容:

In this talk, we will describe an energy minimizing problem arising from seeking the optimal configurations of a class of nematic liquid crystal droplets. More precisely, the general problem seeks a pair  $(\Omega, u)$ that minimizes the energy functional: $$E(u,\Omega)= \int_\Omega \frac12|\nabla u|^2+ \mu \int_{\partial\Omega} f(x,u(x)) d\sigma,$$ among all open set $\Omega$ within the unit ball of $\mathbb R^3$ , with a fixed volume, and $u\in H^1(\Omega,\mathbb S^2)$. Here $f:\mathbb R^3\times \mathbb R \to\mathbb R$ is a suitable nonnegative function, which is given.

While the existence of minimizers remains open in the full generality, there has been some partial progress when $\Omega$ is assumed to be convex.

In this talk, I will discuss some results for $\Omega$ that are not necessarily convex. This is a joint work with my student Qinfeng Li.

报告人简历:

Changyou Wang received his PhD at Rice University at 1996, and is currently a Professor of Mathematics at Purdue University. His research interests are nonlinear partial differential equations arising from geometric variational problems, calculus of variations, and applied mathematics.

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数学与统计学院

2017-06-05

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