The module introduces to the theory of variational minimization problems, which are mostly set in spaces of weakly differentiable functions.
Model problems (brachistochrone, Dirichlet energy, minimal surfaces, etc.), convex integrands and generalizations, existence and uniqueness of minimizers by direct methods, necessary and sufficient (PDE) conditions for minimizers, generalized minimizers (via relaxation or Young measures), problems with constraints, variational principles and applications, duality theory, outlook on regularity.