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MATH-437: Calculus of variations

Summary

Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet energy, p-energy, etc).

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/calculus-of-variations-MATH-437

Moodle Page

http://go.epfl.ch/MATH-437

About this result

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Summary

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/calculus-of-variations-MATH-437

Moodle Page

http://go.epfl.ch/MATH-437

About this result

Ontological neighbourhood

Mathematics

Analysis: Functional analysis

Lectures in this course (12)

Legendre Transform Log in to Mediaspace to watch this video

Explores the Legendre transform, duality in convex analysis, and optimization problems.

Euler-Lagrange Equation Log in to Mediaspace to watch this video

Explores the classical methods for solving optimization problems, emphasizing the Euler-Lagrange equation and its variants.

Regularity in 1D Log in to Mediaspace to watch this video

Explores regularity in 1D functions, emphasizing weak derivatives and minimizers.

Regularity in Higher Dimension Log in to Mediaspace to watch this video

Explores regularity in higher dimensions for scalar problems and discusses weak sense solutions and interior regularity.

Lagrange Multiplier and DuBois-Reymond Equation Log in to Mediaspace to watch this video

Explores Lagrange multiplier method and DuBois-Reymond equation in optimization.

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