# MA8105 Nonlinear PDEs and Sobolev spaces · Spring 2021

## Messages

• (2021-01-21) The lectures starting on Thu, 28 Jan will be physical and take place at Gløshaugen.

## Lectures

• 14 Jan (Harald): Some inequalities from Ch 1. 2.1: Basics on norms, completeness, inner products, bounded linear maps, dual spaces, bidual. Also outlined the proof of the Hahn–Banach theorem (app. A).
In the video recording, the right edge is obscured. Use the notes transcript to see the missing part.
Panopto video link, raw notes transcipt
• 15 Jan (Harald): 2.1: A bestiary of sequence spaces, Hölder's inequality (and when it is an equality), Riesz representation theorem. Weak convergence, a quick look at Banach–Steinhaus (no proof), a brief look at the wild nature of the dual of $\ell^\infty$.
In the video recording, the right edge is obscured. Use the notes transcript to see the missing part.
Panopto video link, raw notes transcript
Recommended exercises: 2–4 on p. 37 (but I covered much of ex 4 in the lecture, actually).
• 21 Jan (Helge): Started with uniform convexity on p. 12. Video and notes: Panopto video link, notes
• 22 Jan (Helge): Started with Prop. 2.9. Covered up to and including Alaoglu, and stopped in the middle of the proof of Prop. 2.20. Panopto video link, notes
• 28 Jan (Harald): Lecture at Gløshaugen!
• 29 Jan (Harald): Lecture at Gløshaugen!