After presenting the classical methods of the Calculus of Variations, the course introduces the direct methods of the Calculus of Variations and discusses numerous applications.
Contents
Classical methods of the calculus of variations: Euler-Lagrange equations and necessary and sufficient conditions for the existence of strong and weak minima for one-dimensional variational problems. Discussion of the Hamiltonian formulation and of the Hamilton-Jacobi equations for one-dimensional problems. After a review of absolutely continuous functions and Sobolev spaces, the direct methods are then discussed. Numerous applications are presented and studied during the course.
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