Elliptic regularity theory

Dates

Tuesday 12-14 in SEM DA green 06B
Friday 10-12 in DA04G10

Preliminary meeting

Monday, 2.10.23 12:00 in DA green 06B

Content

The lecture (3h/week) introduces to the regularity analysis of elliptic partial differential equations. We plan to discuss

shift theorems for elliptic PDEs (and systems)
regularity theory in corner domains, where the classical shift theorem breaks down and weighted spaces are the appropriate tool
Hölder regularity for scalar equations with \(L^\infty\)-coefficients (De Giorgi-Nash-Moser theorem)

We will also introduce the various tools that are needed for the analysis such as Morrey and Campanato spaces as well as appropriate interpolation spaces

Class notes

Chapter 1 + 2

Literature

Gilbarg-Trudinger: elliptic PDEs of second order
Giaquinta-Martinazzi: an introduction to the regularity theory for elliptic systems
Jost: PDEs

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