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:  //cern.zoom.us/j/66384139585?pwd=T2didUg1TFZoNFNNOWhFa0hqeThqUT09

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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。