报告名称：Reverse Agmon Estimates

报告专家：吴先超

专家所在单位：武汉理工大学数学系

报告时间：2021年09月28日9：00-11：00

报告地点：威廉希尔201学术报告厅

专家简介：吴先超，加拿大McGill大学博士。研究方向为半经典分析在偏微分方程中的应用，主要研究特征函数的渐近估计问题。已经在Annales Henri Poincare等国际期刊上发表论文。

报告摘要：We consider L^2-normalized eigenfunctions of the semiclassical Schrodinger operator on a compact manifold. The well-known Agmon-Lithner estimates are exponential decay estimates (ie. upper bounds) for eigenfunctions in the forbidden region. The decay rate is given in terms of the Agmon distance function which is associated with the degenerate Agmon metric with support in the forbidden region.

Inthis talk, first we will introduce a partial converse to the Agmon estimates (ie. exponential lower bounds for the eigenfunctions) in terms of Agmon distance in the forbidden region under a control assumption on eigenfunction mass in the allowable region arbitrarily close to its boundary. Then by considering a Neumann problem with applying Poisson representation and exterior mass estimates on hypersurfaces, we will prove an improved reverse Agmon estimate on a hypersurface in the analytic setting.

邀请人：陈立

（审核：郑大彬）