Analysis and PDE Seminar Homepage, Spring 2013

Location: 383N

Time: Thursday, 2:15-3:15pm.

  • Wednesday, April 10, 2:30pm in 383N and 4pm in 380X, Bay Area Microlocal Analysis seminar at Stanford

    Nicolas Burq (Orsay)

    ``Micro-local analysis of the Dirichlet-Neumann operator''

    Abstract: 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. Zuily.

    and

    Michael Hitrik (UCLA)

    ``Spectra and subelliptic estimates for operators with double characteristics''

    Abstract: 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 surfaces''