A selection out of the following: Model problems and examples (Dirichlet energy, isoperimetric and brachistochrone problems, minimal surfaces, Bolza and Weierstrass examples, …), existence and uniqueness of minimizers by direct methods, weak lower semicontinuity of (quasi)convex variational integrals, necessary and sufficient (PDE) conditions for minimizers, problems with constraints (obstacles, capacities, manifold and volume constraints, ...), generalized minimizers (relaxation, Young measures, ...), variational principles and applications, duality theory, outlook on regularity. |
