报告人：Giuseppe Buttazzo
时间：2021年7月15日（星期四）下午3:00-4:00
地点：Zoom Link: https://cern.zoom.us/j/66384139585?pwd=T2didUg1TFZoNFNNOWhFa0hqeThqUT09
zoom会议号 : 663 8413 9585
密码 : 499561
邀请人：李沁峰
TITLE: Upper and lower bounds for some shape functionals
ABSTRACT:The relations between two quantities related to the Laplace operator are considered.
In particular, taking as a model the heat diffusion, governed by the heat equation, we aim to study
the relations between the average temperature of a heated body and the temperature decay rate of
the body in absence of heat sources. The quantities above are expressed by the so-called
"torsional rigidity" and by the principal eigenvalue of the Laplace operator. The relations
above are studied in the classes of general domains, convex domains, and domains with a small thickness.
This allows to obtain a detailed description of the Blasche-Santaló diagram of the two quantities.
Several open questions are discussed, in particular when the Laplacian is replaced by the
$p$-Laplacian.
报告人简介：Giuseppe Buttazzo，是偏微分方程、区域优化和椭圆算子谱理论领域著名的学者，在JEMS、ARMA、JMPA、
SIAM J. Math. Anal.、JFA等高水平杂志发表近两百篇文章，被引用3000多次。
