Calculus of Variations

The course aims at providing an introduction to the modern theory of Calculus of Variations, which is a powerful tool to study many problems in mathematics, physics and applied sciences (for instsance: existence of geodesics, surfaces of minimal area, periodic solutions of N-body problems, existence of solutions for nonlinear elliptic PDE).

Acquisition of the basic notions and techniques in the theory of Calculus of Variations: minimization, deformations, problems of compactness, relations between topology and critical points. Study of the relations between critical point theory and partial differential equations.