Analysis and PDE Seminar Homepage, Spring 2013
Time: Thursday, 2:15-3:15pm.
Wednesday, April 10, 2:30pm in 383N and 4pm in 380X,
Bay Area Microlocal Analysis seminar at
Nicolas Burq (Orsay)
``Micro-local analysis of the Dirichlet-Neumann operator''
It is well known that the Dirichlet Neumann operator in a smooth domain
is a pseudo-differential operator. On the other hand, the definition of
this operator requires actually only very low regularity (namely it is
defined as soon as the domain is Lipshitz). In this talk I will present
some recent results describing the micro-local nature of the Dirichlet
Neumann operator in rough domains . Our results depend of course on the
level of smoothness we assume on the domain, but the micro-local
description that involves para differential operators we get is non
trivial as soon as the domain is better than Lipshitz. Furthermore,
motivated by the analysis of the water-waves system, we work in the
framework of uniformly local Sobolev spaces rather than the usual
(L^2-based) Sobolev setting. This is a joint work with T. Alazard and C.
Michael Hitrik (UCLA)
``Spectra and subelliptic estimates for operators with double
For a class of non-selfadjoint semiclassical operators with double
characteristics, we give complete asymptotics for low-lying eigenvalues and
establish accurate semiclassical resolvent estimates of subelliptic type in
a neighborhood of the origin. The assumptions along the double
characteristics generalize those valid for operators of
Kramers-Fokker-Planck type. This is joint work with Karel Pravda-Starov.
Monday, April 15, 2:30pm in Room 381U (Note unusual day/time/room):
Sergiu Klainerman (Princeton)
``A non-isotropic result on the formation of trapped