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Calculus of Variations and Multiscale Analysis

  • Homogenization of variational problems
  • Gamma-Convergence and relaxation
  • Variational methods in continuum mechanics
  • Variational methods in rate independent evolution prooblems
  • Variational methods in phase transitions
  • Variational methods in micromagnetics
  • Applications of geometric measure theory
  • Existence problems in the calculus of variations
  • Hamilton-Jacobi equations



Direct methods in the calculus of variations:

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


Spaces with Ricci curvature bounded from below

Aim of the course is to be an introduction to the study of `metric measure spaces with Ricci curvature bounded from below'. Preliminaries are measure theory and some knowledge of Riemannian geometry. Then I will discuss:


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