CNA-PIRE Working Group: Spring 2013

The first meeting will take place on Tuesday, January 22nd, at 2:30 pm.

CNA Working Group on Calculus of Variations

TITLE: Selected Topics on Calculus of Variations: Relaxation Theory,
Gamma-Convergence, Discrete to Continuum Models, and Beyond

Organizers: Irene Fonseca and Giovanni Leoni

When/Where: Tuesdays 2:30-3:30, Wean Hall 7218

Participants will be invited to give informal presentations on the
following topics.

1. Relaxation Theory

(i) Irene Fonseca will initiate the discussion by presenting
contemporary methods in relaxation theory.

(ii) Relaxation for Unbounded Integrands.

Suggested reading material includes (and references therein):

* Ben Belgacem, Hafedh, Relaxation of singular functionals defined
on Sobolev spaces. ESAIM Control Optim. Calc. Var. 5 (2000), 71–85
* Anza Hafsa, Omar; Mandallena, Jean-Philippe,
Relaxation theorems in nonlinear elasticity. Ann. Inst. H. Poincaré
Anal. Non Linéaire 25 (2008), 135–148.

2. Gamma-Convergence

1-2 sessions on the theory of Gamma-convergence.

Suggested reading material includes:
Dal Maso, Gianni, An Introduction to Gamma-Convergence, Birkhauser, 1992

3. Discrete to Continuum Models

Suggested reading material includes (and references therein):
* Blanc, X.; Le Bris, C.; Lions, P.-L. From molecular models to
continuum mechanics. Arch. Ration. Mech. Anal.  164 (2002), 341–381
* Alicandro, Roberto; Braides, Andrea; Cicalese, Marco,
Continuum limits of discrete thin films with superlinear growth
densities. Calc. Var. Partial Differential Equations 33, 267–297.

4. Singular Perturbed Problems (as time permits)