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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


Topics in the Calculus of Variations

The course is subdivided in three parts, which may vary in size and content according to the interests of the audience. 1. Nonlocal discrete systems. We consider simple boundary value problems on sets of integers depending on a function minimizing a nonconvex interaction potential and a long-range convex energy. Our goal is to describe the interaction between nonconvexity and nonlocality through asymptotic properties of solutions and of minima as the size of the domain of minimization diverges.


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