報(bào)告題目： Lower Bounds for the First Eigenvalue of the Vibrating Clamped Plate under Compression
報(bào)告時(shí)間： 2015年 8月19日（周三）上午 10：00-11：00
報(bào)告地點(diǎn)： 中關(guān)村校區(qū)中心教學(xué)樓843（或844）教室

Abstract:   We give a sharp lower bound to the fundamental frequency of a clamped vibrating plate under compress in  the context of plates of different shapes of fixed area.  Mathematically, the problem is that of bounding the first eigenvalue of a certain 4th-order partial differential operator with leading term the bi-Laplacian from below by a positive constant over the square of the domain's area.  We give a Rayleigh-Faber-Krahn-type result for this problem.  (This is joint work with R. Benguria and R. Mahadevan.)  

報(bào)告人簡(jiǎn)介： Professor Mark S. Ashbaugh 在Laplace的特征值及等周不等式方面做出了杰出的工作， 曾解決了著名的PPW猜想、二維及三維的Rayleigh猜想等。在《Annals of Mathematics》、《Bulletin of American mathematical Society》、《Duke Math. J.》、《Advances in Mathematics》、《Comm. Math. Phys.》等國(guó)際一流雜志上發(fā)表數(shù)十篇論文。