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MATH-502: Distribution and interpolation spaces

Summary

The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial differential equations (PDE).

Lectures

Instructor

Alexis Paul Benjamin Michelat

Après avoir soutenu ma thèse en 2019 à ETH Zürich sous la direction de Tristan Rivière , je fus postdoc de la Fondation Sciences Mathématiques de Paris à l'Université de Paris (nouveau nom de l'Université Paris-Diderot) pendant une année sous la supervision de Frédéric Hélein , et je fus ensuite un postdoc financé par le FNS (via le Early Postdoc Mobility) à l'Université d'Oxford sous la supervision d' Andrea Mondino . Depuis le 1er septembre 2022, je suis Instructeur Bernoulli à l'EPFL (Lausanne).

Official source

https://edu.epfl.ch/coursebook/en/distribution-and-interpolation-spaces-MATH-502

Moodle Page

http://go.epfl.ch/MATH-502

About this result

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Summary

Lectures

Instructor

Alexis Paul Benjamin Michelat

Official source

https://edu.epfl.ch/coursebook/en/distribution-and-interpolation-spaces-MATH-502

Moodle Page

http://go.epfl.ch/MATH-502

About this result

Lectures in this course (28)

Normed Spaces & Reflexivity Log in to Mediaspace to watch this video

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Distributions & Interpolation Spaces Log in to Mediaspace to watch this video

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Interpolation Techniques Log in to Mediaspace to watch this video

Explores interpolation techniques, including inequalities, continuity proofs, and function interpolation in different spaces.

Interpolation Spaces Log in to Mediaspace to watch this video

Explores interpolation spaces between Banach spaces and real interpolation spaces.

Interpolation Theory: Embedding and Completeness Log in to Mediaspace to watch this video

Covers the embedding of spaces and the completeness of spaces, exploring the connection between interpolation theory and approximation theory.

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