Extremum Problems for Laplacian Eigenvalues

Professor
Fanghua Lin
Silver Professor, Courant Institute of Mathematical Sciences,
New York University
Fellow, American Academy of Arts and Sciences
(Poster)
(Photo)

Date: 
5 December 2014 (Friday) 
Time: 
4:30pm
 5:30pm (Preceded by Reception at 4:00pm) 
Venue: 
1/F Shiu Pong Hall,
Ho Sin Hang Campus, Hong Kong Baptist University



Abstract
Eigenvalue Problems for Laplacians are among most wellknown problems in classical analysis, partial differential equations, calculus of
variations and mathematical physics. In this lecture I shall discuss a
couple very basic extremum problems involving eigenvalues of the
Laplacian. Such problems arise in shape optimizations, pattern
formations
and other studies in science, and solutions to these problems
have been challenging for a very long time. In particular, we shall
see how classical RayleighFaberKrahn inequalities and Weyl's
asymptotic formula along with theorems concerning nodal domains coming
into play in understanding of these problems. The lecture would be a
brief and elementary survey of some of recent results.


All
are welcome 

