After successful completion of the course, students are able to...

• solve homogeneous and inhomogeneous elliptic boundary value problems in the context of Sobolev space theory;
• apply the Fourier transform to distributions;
• define Sobolev spaces of arbitrary order on domains;
• apply results on embeddings, extensions and traces of Sobolev functions;
• describe and partially apply the ideas and methods which are used in proving the central results..

• Distributions and their Fourier transform
• Sobolev spaces of arbitrary real order on the whole space
• Sobolev spaces on domains
• Elliptic operators in L_2 (a priori estimates, existence and uniqueness of solutions, regularity)
• Spectral theory of elliptic operators (if time permits)

During the lecture the contents are presented; these are discussed together and questions are answered.

Die Vorlesung findet auf Zoom statt.

Link für die 1. Einheit und Vorbesprechung am Donnerstag, 4. 3., 10:00-11:30:

https://tuwien.zoom.us/j/97668704935?pwd=WGxXT2xuaGJGdkRjYVdzeElPZTVNQT09

(Meeting ID: 976 6870 4935, Password: 9Epsmaz3)

Weitere Termine wöchentlich nach Vereinbarung.

Oral exam.

Prerequisites from analysis 3, functional analysis and partial differential equations will be used.