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

• January 17

  A survey on \Gamma-convergence       Notes (pdf - 686Kb)

  Riccardo Cristoferi

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• January 24

  G-convergence - basic properties       Notes (pdf - 686Kb)

  Riccardo Cristoferi

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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

  H-convergence and \Gamma-convergence       Notes (pdf - 182Kb)

  Matteo Rinaldi

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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

  Nonlinear stochastic homogenization       Notes (pdf - 220Kb)

  Peter Gladbach

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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