25 Mar 2008; * Mat-Nat
Faculty (UiTø), room A228.
Tuesday 11:15-13:00
(notice time/date)*

Andrea Braides (University Roma 2, Italy)

"The use of Gamma-convergence in the analysis of multi-scale problems".

Gamma-convergence is a very useful tool for the description of complex variational problems involving small parameters (as in homogenization, phase transitions, atomistic systems, etc.). The underlying idea of the Gamma-convergence approach is to substitute an energy with a complex dependence on a small parameter by another one where the dependence on this parameter has been averaged out (Gamma-limit), or simplified (Gamma-development). The resulting energy `justified by Gamma-convergence' may however fail to represent the relevant behavior of the original energy in its sensitiveness on relevant external parameters (boundary conditions, forcing terms, etc.) or be of a type different from a desired form commonly used by practitioners.

I will present some proposals on how to modify the use of Gamma-convergence to overcome (some of) those drawbacks. These proposals are based on the notions of `uniform equivalence by Gamma-convergence' and of `singular parameters' for the Gamma-limit, introduced to this end.