[CvGmt News] Colloquium Yann Brenier

[buttazzo at dm.unipi.it]

Vi informo che giovedi 21 ci sara' un "Colloquium" del Dipartimento di 
Matematica, tenuto da Yann Brenier, uno dei piu' noti specialisti in PDE e 
teorie cinetiche. Come per tutti i "colloquia" l'esposizione sara' di tipo non 
specialistico.

Tutti gli interessati sono invitati a partecipare. Seguira' un piccolo rinfresco 
nel locale adiacente l'aula magna.

Giuseppe Buttazzo


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