報(bào)告題目：Bounds of nodal sets of eigenfunctions

報(bào)告人：朱久義（Louisiana State University）

報(bào)告時(shí)間：2021年12月15日上午11:00-12:30

騰訊會(huì)議ID：510 463 682

報(bào)告人簡(jiǎn)介：朱久義, 路易斯安那州立大學(xué)助理教授。2008年碩士畢業(yè)于湖南師范大學(xué), 2013年博士畢業(yè)于韋恩州立大學(xué),。2013-2016年在約翰霍普金斯大學(xué)擔(dān)任J.J. Sylvester Assistant Professor. 主要研究方向是偏微分方程,。兩次獲得美國(guó)自然科學(xué)基金資助,，獨(dú)立PI. 在AJM, ARMA, Analysis & PDE, CPDE等雜志上發(fā)表多篇論文,。

報(bào)告摘要：Motivated by Yau's conjecture, the study of the measure of nodal sets (Zero level sets) for eigenfunctions has been attracting much attention. We investigate the measure of nodal sets for Steklov, Dirichlet and Neumann eigenfunctions in the domain and on the boundary of the domain. For Dirichlet or Neumann eigenfunctions  in the analytic domains, we show some sharp upper bounds of  nodal sets  which touch the boundary. We will also discuss some upper bounds of nodal sets for  eigenfunctions of general eigenvalue problems arising from Chladni patterns, which were discovered more than 200 years ago. Furthermore, some recent study of nodal sets in periodic elliptic homogenization will be discussed. Part of the talk is based on joint work with Carlos Kenig, Fanghua Lin and Jinping Zhuge.

邀請(qǐng)人：謝君輝

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