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Gamma-convergence

Lecturer: 
Gianni Dal Maso
Course Type: 
PhD Course
Academic Year: 
2016-2017
Period: 
October-February
Duration: 
60 h
Description: 

Direct methods in the calculus of variations:

  • semicontinuity and convexity,
  • coerciveness and reflexivity,
  • relaxation and minimizing sequences,
  • properties of integral functionals.

Gamma-convergence:

  • definition and elementary properties,
  • convergence of minima and of minimizers,
  • sequential characterization of Gamma-limits,
  • Gamma-convergence in metric spaces and Yosida transform,
  • Gamma-convergence of quadratic functionals.

G-convergence:

  • abstract definition,
  • connection with Gamma-convergence,
  • convergence of eigenvalues and eigenvectors.

The localization method for Gamma-convergence:

  • Increasing set functions and their regularizations,
  • measures, fundamental estimate for subadditivity,
  • integral representation of Gamma-limits,
  • compactness of elliptic operators with respect to G-convergence,
  • homogenization problems for convex integral functionals,
  • homogenization of elliptic operators.
Location: 
A-133

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