Mathematics

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.