Calculus of Variations is that area of mathematics defined from the following problem: determine,
in a given family of objects, the one that minimize (or maximize) a certain quantity. Such objects can
be functions, curves, surfaces, or other. The aim of the course is that of giving an introduction of the
subject and to present the main classical problems. More precisely we will focus on:
Classical methods: Euler-Lagrange equation, hamiltonian formulation, Hamilton-Jacobi equation;
Direct methods: the Dirichlet integral, existence theorems, relaxation theory;
Regularity theory;
Minimal surfaces: parametric and non-parametric formulations, the classical Plateau problem, existence of solutions via Douglas-Rado approach;
Isoperimetric inequality in dimension 2.
Link zum Modulhandbuch Mathematik