Ph D course: Variational problems
for local minima.
(Problemi variazionali per minimi locali) (prof.
March 29-May 31 2012 ON THURSDAYS
11:00-13:30 IN ROOM B
These are the notes of the course, which I posted as soon as
possible. This means that they are full of mistakes and
misprints; please let me know as soon as you find them. The
file will be corrected after your remarks.
In the last page of the notes you can find a list of
problems to solve. You are suggested to organize the work in pairs.
DATES OF THE EXAMS
July session: July 9-July 20
September session: from Sept 10
Description of the course
We have examined some issues on the description of sequences
of energies with local minima. It is known that "coarse grained"
theories, eg those obtained by Gamma-convergence, in general do not
describe those local minima, or their effect on gradient flows of those
enegies. We will focus then on:
1) some examples when a desciption of local minima of complex systems
is possible thanks to a simpler energy which captures the main features
of the systems;
2) elaboration of criteria that ensure the passage to the limit for
"stable solutions" or local minimizers;
3) evolution problems for energies with many local minima obtained by a
time-discrete scheme (minimizing movements along a sequence of