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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.

Page manager: karin.johansson@liu.se
Last updated: 2022-11-15