Calculus of Variations and some Optimal Control/
Number of credits: 4 hp
Examiner: Gunnar Aronsson
Course literature: Own material.
Course contents: Euler-Lagrange equations in some classical cases. Counterexamples for existence. Semi-classical approach by Tonelli. Existence and regularity theorems. Direct methods. Importance of lower semi-continuity. Dirichlet integral and Laplace equation. P-Dirichlet integral and p-Laplace equation. Minimal surface equation; Mumford-Shah functional; generalized E. equations for some minimax problems; infinity Laplace equation. Variational system for ODE. "Spike" and "multispike" perturbations. Basic perturbation formula; perturbation cone. Brouwer´s fixed point theorem and a covering principle for continuous mappings. Barycentric coordinates. Pontryagin´s maximum principle in various cases. What is a switch?
Organisation: Lectures and (as part of examination) exercises.
Examination: Exercises (assignments).
Prerequisites: Analysis and integration theory.
Last updated: 2022-11-15