Dottorato di Ricerca in Matematica - UniversitÓ di Pavia
Ph D course: Local
minimization, variational evolution and Gamma-convergence
(prof. Andrea Braides)
Description of the course
We examine some issues on the description of sequences
of energies with local minima. It is known that "coarse grained"
theories (e.g. those obtained by Gamma-convergence) in general
do not describe those local minima or their effect on the
related gradient flows. We focus then on:
1) some examples when a description 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 energies).
The notes of the course have been 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.
A slightly different (and corrected) version of the notes is
contained in the book A. Braides. Local minimization,
variational evolution and Gamma-convergence. Lecture Notes in
Mathematics. Vol. 2094. Springer, Berlin, 2013.
If you need to quote results from the notes, please quote that
book, following the numbering therein.