Special Topics in Analysis

Next lectures
12.11.2025, 09:15 (Seminargebäude 3-14)
19.11.2025, 09:15 (Seminargebäude 3-14)
26.11.2025, 09:15 (Seminargebäude 3-14)
03.12.2025, 09:15 (Seminargebäude 3-14)
10.12.2025, 09:15 (Seminargebäude 3-14)
17.12.2025, 09:15 (Seminargebäude 3-14)
07.01.2026, 09:15 (Seminargebäude 3-14)
14.01.2026, 09:15 (Seminargebäude 3-14)
21.01.2026, 09:15 (Seminargebäude 3-14)
28.01.2026, 09:15 (Seminargebäude 3-14)
04.02.2026, 09:15 (Seminargebäude 3-14)

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The plan of the lecture is to give overviews and proofs of some special topics in regularity theory of (non-linear) PDE and the Calculus of Variations.

In the first part of the lecture we will discuss the De Giorgi-Nash-Moser scheme including the very weak Harnack and weak Harnack inequalities. We will continue with degenerate equations. Thereafter, possible topics are Evan's proof of the $C^{1,\alpha}$-regularity for the $p$-Laplacian or Savin's proof of the continuity of solutions to degenerate equations in 2D.

I am also open to any other suggestions.

Keywords
PDE, Calculus of Variations, Regularity theory

Prerequisites
PDE 1+2, Functional analysis, Measure theory

Audience
graduate students, PhD students, PostDocs

Language
english