学术报告（偏微分方程讨论班）


报告题目: A characterization of optimal two-phase multifunctional composite designs (多功能复合材料的最优设计)

演讲人： Dr. Luis Silvestre
Courant Institute of Mathematical Sciences，New York University

时间： 2007年6月5日（星期二）下午4：00-5：00

地点： 理科大楼A座1510室。

Abstract: We will discuss the problem of optimal design of a two-phase composite material to maximize the sum of thermal and electric conductivity. There was some numerical evidence that the optimal design was related to a periodic minimal surface. We obtain a characterization of an optimal configuration in terms of a free boundary type problem and show what the free boundary cannot be such minimal surface. In the process of obtaining this result, we provide a new proof of the relevant case of Bergman’s cross-property bound. With the same idea a simple new proof of the Hashin-Strikman bounds can also be obtained.