Fine Properties of Sobolev Functions

What it is about

You will learn fundamentals and further properties of Sobolev functions. Starting with weak derivatives, you will treat approximations by smooth functions, traces and extension theorems, as well as compact embeddings. In addition, finer properties such as precise representatives, quasi-continuity and differentiability on lines are shown using measure-theoretic techniques (e.g. Hausdorff measures and capacity). At the end you will be able to apply and explain these concepts and proof methods.

What you will be able to do

• Understanding of weak derivatives and Sobolev spaces
• Relation between Lipschitz and Sobolev functions
• Knowledge of trace, extension and compact embedding theorems
• Familiarity with Hausdorff measures and capacity theory
• Applying measure-theoretic techniques to prove fine properties (e.g. quasi-continuity)

What the module consists of

• VorlesungVermittlung der Theorie und Beweismethoden; Hauptformat der Lehre

Teaching method

• Blackboard lecturesErläuterung und Herleitung der Konzepte und Beweise