The use of variational techniques in the study of sequences of elliptic operators
The aim of this working group is to give a broad overview of the use of variational techniques that are used to treat sequences of elliptic problems.
Each subtopic is intended to be selfcontained and presented first from a heuristic point of view and then from a technical one (no all the details of the proofs!),
in order to give the participants the flavor of the idea behind the arguments used in the articles that will be discussed.
The page of the working group in the CNA website can be found here.
Schedule

January
17


January
24


January
31
Gconvergence  relation with \Gammaconvergence
(see file above)
Riccardo Cristoferi


February
7
Hconvergence  definition and main properties
Notes (pdf  287Kb)
Giovanni Gravina


February
14


February
21
The idea behind the variational structure of Hconvergence
Notes (pdf  148Kb)
Matteo Rinaldi


February
28
Linear elliptic problems in varying domains  Part 1
Notes (pdf  243Kb)
Laurent Dietrich


March
7
Linear elliptic problems in varying domains  Part 2
Notes (pdf  256Kb)
Laurent Dietrich


March
21
Linear elliptic problems with simultaneously varying operators and domains
Notes (pdf  260Kb)
Marco Caroccia


March
28
Homogenization, Asymptotic Expansion and 2Scale Convergence  Part 1
Notes (pdf  190Kb)
Adrian Hagerty


April
4
Homogenization, Asymptotic Expansion and 2Scale Convergence  Part 2
Notes (pdf  210Kb)
Adrian Hagerty


April
11
Homogenization of nonlinear elliptic operators
Notes (pdf  213Kb)
Janusz Ginster


April
18
Stochastic homogenization of linear elliptic equations in divergence form  Part 1
Notes (pdf  147Kb)
Samuel Cohn


April
25
Stochastic homogenization of linear elliptic equations in divergence form  Part 2
Notes (pdf  118Kb)
Samuel Cohn


May
2


May
2
Material
G. Allaire, Homogenization and twoscale convergence,
pdf
S. Armstrong and C.K. Smart, Stochastic homogenization of fully nonlinear uniformly elliptic equation revisited,
pdf
N. Ansini and G. Dal Maso and C.I. Zeppieri, \Gammaconvergence and Hconvergence of linear
elliptic operators,
pdf
G. Dal Maso, An introduction to \Gammaconvergence,
link
G. Dal Maso and A.Defranceschi, Limits of nonlinear Dirichlet problems in varying domains,
pdf
G. Dal Maso and A. Garroni, New results on the asymptotic behavior of Dirichlet problems in perforated domains,
pdf
G. Dal Maso and L. Modica, Nonlinear stochastic homogenization,
pdf
G. Dal Maso and L. Modica, Nonlinear stochastic homogenization and ergodic theory,
pdf
G. Dal Maso and F. Murat, Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains,
pdf
G. Dal Maso and I.Skrypnik, Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains,
pdf
L. C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations,
pdf
F. Murat and L. Tartar, Hconvergence,
pdf