ETH :: D-MATH :: Analysis Seminar

This work is about the Cauchy theory for the water waves equations. Our main result is that, after suitable paralinearizations, the system can be arranged into an explicit symmetric system of Schroedinger type. We then show that the smoothing effect and Strichartz estimates for the (one dimensional) surface tension water waves as a consequence of this reduction. We are able to obtain sharp results in terms of regularity of the indexes of the initial data, and weights in the estimates (work in collaboration with Nicolas Burq and Claude Zuily)

Speakers:

Thomas Alazard (Paris Orsay)

Homepage: http://www.math.u-psud.fr/~alazard/

Mar. 9, 2010

Yuxin Ge

Regularity of optimal transportation maps on compact locally nearly

15:15-16:15

Abstract:

Given a couple of smooth positive measures of same total mass on a
compact connected Riemannian manifold M, we look for a smooth optimal
transportation map G, pushing one measure to the other at a least total
squared distance cost, directly by using the continuity method to
produce a classical solution of the elliptic equation of Monge-Ampere
type satisﬁed by the potential function u, such that G=exp(grad u). This
approach boils down to proving an a priori upper bound on the Hessian of
u. In this talk, based on the recent local C^2 estimate of
MaTrudinger-Wang, we treat the case of manifolds with curvature
suﬃciently close to 1 in C^2 norm.

Speakers:

Yuxin Ge (University of Creteil-Paris 12)

E-Mail:

Homepage: http://perso-math.univ-mlv.fr/users/ge.yuxin/

Mar. 16, 2010

Bernhard Ruf

Blow-up solutions for critical Trudinger-Moser equations in R^2

15:15-16:15

HG G 43

Abstract:

Speakers:

Prof. Bernhard Ruf (University of Milan (Italy))

E-Mail:

Apr. 13, 2010

Walter Craig

15:15-15:15

Speakers:

Walter Craig (Mc Master University)

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