The course will take place on:

wednesdays at 4:30-6 pm

Venue: IAC (Istituto per le Applicazioni del Calcolo `M. Picone') in viale del Policlinico 137 (see map).
 

Program

1. Definitions and general properties of Gamma-convergence. The direct method
2. Segmentation problems. Subadditivity.
3. Elliptic problems. Convexity.
4. Homogenization problems. Oscillations
5. The gradient theory of phase transitions.
6. Continuous limits of difference schemes.
7. Free-discontinuity problems.

The course will be based on a number of one-dimensional examples, which will allow us to introduce various arguments of the calculus of variations (direct methods, weak convergences, convex analysis, convergence of measures, functions with bounded variations, etc.). Some seminars will conclude the course on higher dimensional problems (such as sets of finite perimeter, Dirichlet problems in perforated domains, dimension-reduction problems).
 

Prerequisites: some measure theory, Lebesgue spaces, basic functional analysis

The text of the lessons will be provided as a pdf file on this site (see the course page in italian).