Lecturer:
Course Type:
PhD Course
Academic Year:
2020-2021
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.
Research Group:
Location:
Online