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MATH-604: Some Aspects of Calculus of Variations

Summary

The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals.

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/some-aspects-of-calculus-of-variations-MATH-604

Moodle Page

http://go.epfl.ch/MATH-604

About this result

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Summary

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/some-aspects-of-calculus-of-variations-MATH-604

Moodle Page

http://go.epfl.ch/MATH-604

About this result

Ontological neighbourhood

Mathematics

Analysis: Functional analysis

Topology: General topology

Lectures in this course (14)

Calculus of Variations: Introduction Log in to Mediaspace to watch this video

Introduces calculus of variations with examples like the Brachistochrone problem in an applied context.

Calculus of Variations: Direct Method Log in to Mediaspace to watch this video

Covers the direct method of the calculus of variations, focusing on the existence of solutions for minimization problems.

Variational Problems: Quasi-Convexity Log in to Mediaspace to watch this video

Explores the theory of quasi-convexity in variational problems from continuum mechanics, discussing its principles, applications, and relationship with convexity.

Variations: Jensen-Type Inequality Log in to Mediaspace to watch this video

Covers the Jensen-Type inequality for young meanres and the connection between young and quasi convexity.

Blow up Technique Log in to Mediaspace to watch this video

Explores the Blow up Technique in Variations, emphasizing its role in establishing boundedness and verifying integral fractional properties.

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