[CvGmt News] Colloquium Yann Brenier
buttazzo at dm.unipi.it
buttazzo at dm.unipi.it
Tue May 19 12:07:25 CEST 2009
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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