[CvGmt News] Seminar Announcement

[depascal at dm.unipi.it]

Si noti l'inizio alle 16:30 (seguira' coffee break)

GIOVEDI' 21 MAGGIO 2009

16:30-17:30, Aula Magna (Dip. Matematica)

COLLOQUIA DI DIPARTIMENTO
HIDDEN CONVEXITY IN SOME NONLINEAR PDEs FROM GEOMETRY AND PHYSICS
Yann Brenier (Universite' de Nice)


The purpose of the talk is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is unrevealed, robust existence and uniqueness results can be unexpectedly obtained for very general data. Of course, as usual,  regularity issues are left over as a hard post-process, but, at least, existence, uniqueness  and stability results are obtained in a large, global, framework. A selected list of cases contains 

THE MONGE-AMPERE EQUATION (solving the Minkowski problem and strongly related to the so-called optimal transport theory since the 1990's)
THE EULER EQUATION  (describing the motion of inviscid and incompressible fluids, interpreted by Arnold as geodesic curves on infinite dimensional groups of volume preserving diffeomorphisms)
 THE MULTIDIMENSIONAL HYPERBOLIC SCALAR CONSERVATION LAWS (a simplified model for multidimensional systems of  hyperbolic conservation laws)
THE BORN-INFELD SYSTEM  (a non-linear electromagnetic model introduced in 1934, playing an important role in high energy Physics since the 1990's).

Some of these cases will be discussed during the lecture.
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You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20090521a/