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 approximation,
• 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.
Rooms:
- 133: 26/11, 17/12, 19/12
- 134: 28/11, 5/12