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【理学院讲坛】数学中心学术报告:北京大学数学科学学院蒋美跃教授学术报告
发布时间:2019-04-23【告诉好友】 【关闭窗口】
主题:Differential Inclusions and Variational Problems in BV Space in Dimension 1
时间:2019年4月25日上午15:00-18:00
地点:理学院数学统计楼213
主讲:蒋美跃 教授
摘要:Let X be a Banach space, E(u) be a convex functional on X, may not be differentiable, F(u)be a C^1 functional. we consider the critical points of the functional E+F. As the functional may not be differentiable, the Euler-Lagrange equation d(E+F)=0 does not make sense in general. One way to overcome this difficulty is to use the subdifferential partial E to replace the differential dE, and consider the differential inclusion 0inpartial E+dF as the Euler-Lagrange equation. In this talk we will discuss some variational problems in BV space, the space of functions with bounded variation in dimension 1. These functionals are related 1-dimensional prescribed mean curvature problem and 1-Laplacian equation. We will illustrate some properties of the critical points in the above sense and show that one can add more restrictions to the critical points of the problem via the variation of the domain. With some conditions on f(x,u), existence of new type critical points of E+F are established.

报告人简介:蒋美跃,北京大学数学科学学院教授、博士生导师。主要研究方向为非线性分析,在Hamilton系统、非线性椭圆方程、非光滑分析以及临界群理论等方面取得了系列重要研究成果。他的主要成果发表在包括 Ann. Inst. H. Poincaré Anal. Non Linéaire; Bull.London Math.Soc.;Manuscripta Math; Calc. Var. Partial Differential Equations; JDE; Sci. China Ser. A等国际知名学术期刊上,特别是在辛几何中关于Lagrange子流形相交问题的Arnold 猜测,带障碍的Hamilton系统周期解问题,ROF泛函极小问题,曲线曲率流自相似解,1-Laplace 方程等方面取得了一系列具有很高学术价值和理论意义的研究成果,受到多位国际知名数学家的高度评价,并被用来解决其它一些重要数学问题。
 
      
      
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