Summary

Introduction to classical Calculus of Variations and a selection of modern techniques.

Content

Keywords

calculus of variations, optimization, minimization, Euler-Lagrange equations, first variation, direct method, Lagrangian,  convexity, lower semicontinuity.

Learning Prerequisites

Required courses

• MATH-200: Analysis III
• MATH-205: Analysis IV
• MATH-303: Measure and integration

Recommended courses

• MATH-301: Ordinary differential equations
• MATH-302: Functional analysis I
• MATH-305: Sobolev spaces and elliptic equations
• MATH-437: Calculus of Variatinos

Learning Outcomes

By the end of the course, the student must be able to:

• Demonstrate proficiency in statements
• Identify use and role of the assumptions
• Recognize which concepts and results could be used in a given context
• Describe concepts and proofs
• Apply theory for specific examples

Teaching methods

Lectures + Exercises

Assessment methods

Oral

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Resources

Bibliography

"Introduction to the Calculus of Variations", B. Dacorogna

"Direct Methods in Calculus of Variations", B. Dacorogna

"Calculus of Variations", J. Jost & X. Li-Jost

"One-dimensional Variational Problems", G. Buttazzo & M. Giaquinta & S. Hildebrandt

"Introduction to the Modern Calculus of Variations", F. Rindler

"Sets of Finite Perimeter and Geometric Variational Prob- lems: An Introduction to Geometric Measure Theory", F. Maggi

"Measure Theory and Fine Properties of Functions", L.C. Evans & R.F. Gariepy

Ressources en bibliothèque

• One-dimensional Variational Problems / Buttazzo
• Introduction to the Calculus of Variations / Dacorogna
• Calculus of Variations / Jost
• Direct Methods in Calculus of Variations / Dacorogna
• Introduction to the Modern Calculus of Variations / Rindler
• Sets of Finite Perimeter and Geometric Variational Prob- lems: An Introduction to Geometric Measure Theory / Maggi
• Measure Theory and Fine Properties of Functions / Evans