中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人： 翁良俊 博士（Shanghai Jiao Tong University）
题 目：The Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
时 间：2022.01.20（星期四）14:30-15 :30
地 点：思源楼S515
摘 要：In this talk, we will discuss the relative Alexandrov-Fenchel inequality. Firstly we introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the n-th quermassintegral and non-decreases the k-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in unit ball. This talk is based on the recent joint work with Prof. Chao XIA.
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报告人： Jiuyi Zhu（Louisiana State University）
题 目：Quantitative uniqueness of elliptic and parabolic equations
时 间：2022.01.24（星期一），上午10:00
地 点：腾讯会议：933 895 539
摘 要：Quantitative uniqueness is characterized by the order of vanishing of solutions, which describes the quantitative behavior of strong unique continuation property. We say the strong unique continuation property holds if vanishing of infinite order of a solution at a point implies that the solution vanishes identically. It is interesting to know how the norms of the potential functions and gradient potentials control the order of vanishing. This topic is also quite related to the study of quantitative properties of Laplace eigenfunctions. We will report some progress about quantitative uniqueness in different spaces for elliptic equations and parabolic equations. Part of the work is joint with Blair Davey.
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