CIME foundation

C.I.M.E. Summer Course

NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS and APPLICATIONS

Cetraro (Cosenza), Italy, June 22 - 28, 2008

Lecturers
S. Bianchini
E. Carlen
A. Mielke
F. Otto
C. Villani
Cetraro
						     (Cosenza)
CIME LECTURES DESCRIPTION SCHEDULE LOCATION POSTER PARTICIPANTS PHOTOS
Organizers
L. Ambrosio
G. Savaré

LECTURES

STEFANO BIANCHINI (S.I.S.S.A.-I.S.A.S., Trieste, Italy)
Transport rays, differential inclusions and applications to Hamilton Jacobi equations
ERIC CARLEN (Rutgers University, USA)
Sharp functional inequalities and nonlinear evolution equations
ALEXANDER MIELKE (W.I.A.S., Berlin, Germany)
Differential, energetic and metric formulations for rate-independent processes
FELIX OTTO (University of Bonn, Germany)
Scaling laws by PDE methods
CEDRIC VILLANI (Ecole Normale Supérieure de Lyon, France)
Optimal transport and curvature
The Lecture Notes of the courses and further information will also be posted.

COURSE DESCRIPTION

The course will focus on some recent interesting development concerning in particular the optimal transport theory, the variational approach to nonlinear evolution equations, functional inequalities, and differential geometry.

Deep results have been obtained during the last decade: a brief (and largely incomplete) account of the main topics, considered in the present course, involves

  • Distances between probability measures induced by optimal transportation problems, according to the formulations of Kantorovich-Rubinstein-Wasserstein, and their link with Hamilton-Jacobi equations.
  • The construction of an ``infinite dimensional (almost) Riemannian'' structure on measures and the interpretation of many (nonlinear) diffusion PDE's as gradient flows.
  • The link between optimal transport, kinetic formulations, and statistical mechanics.
  • Entropy/Entropy dissipation methods for studying nonlinear evolution equations and functional inequalities.
  • The interplay between geometric properties of the underlying domains (usually ``nice'' Riemannian manifolds) and the probability spaces constructed on them.
  • Geometric inequalities in the framework of non-smooth Metric-Measure Spaces.
  • The metric/energetic theory for gradient flows and rate-invariant evolution problems.

SCHEDULE

The course will start on

    Monday 23 in the morning
and will end on
    Saturday 28 at noon.
Each series of lectures will last 5/6 hours. Participants are supposed to arrive on Sunday 22.

PRELIMINARY PROGRAM

APPLICATION

Application can be submitted on-line directly on CIME web page

    from November 1, 2007. Deadline is April 30, 2008.

A limited finantial support for young participants is available through the CIME foundation.

ORGANIZERS

The poster of the course in PDF