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 sub-topic is intended to be self-contained 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
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January
17
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January
24
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January
31
G-convergence - relation with \Gamma-convergence
(see file above)
Riccardo Cristoferi
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February
7
H-convergence - definition and main properties
Notes (pdf - 287Kb)
Giovanni Gravina
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February
14
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February
21
The idea behind the variational structure of H-convergence
Notes (pdf - 148Kb)
Matteo Rinaldi
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February
28
Linear elliptic problems in varying domains - Part 1
Notes (pdf - 243Kb)
Laurent Dietrich
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-
March
7
Linear elliptic problems in varying domains - Part 2
Notes (pdf - 256Kb)
Laurent Dietrich
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March
21
Linear elliptic problems with simultaneously varying operators and domains
Notes (pdf - 260Kb)
Marco Caroccia
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March
28
Homogenization, Asymptotic Expansion and 2-Scale Convergence - Part 1
Notes (pdf - 190Kb)
Adrian Hagerty
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April
4
Homogenization, Asymptotic Expansion and 2-Scale Convergence - Part 2
Notes (pdf - 210Kb)
Adrian Hagerty
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April
11
Homogenization of non-linear elliptic operators
Notes (pdf - 213Kb)
Janusz Ginster
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April
18
Stochastic homogenization of linear elliptic equations in divergence form - Part 1
Notes (pdf - 147Kb)
Samuel Cohn
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April
25
Stochastic homogenization of linear elliptic equations in divergence form - Part 2
Notes (pdf - 118Kb)
Samuel Cohn
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May
2
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May
2
Material
G. Allaire, Homogenization and two-scale 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, \Gamma-convergence and H-convergence of linear
elliptic operators,
pdf
G. Dal Maso, An introduction to \Gamma-convergence,
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, H-convergence,
pdf