- extension of integration theory (convergence theorems, Lp-spaces, partial integration),
- construction of Sobolev spaces,
- analysis in Sobolev spaces (convolution, Dirac sequences, partition of unity, dense sets of functions),
- applications to partial differential equations (Poincaré inequality, fundamental lemma of calculus of variations, weak formulation of boundary problems),
- Sobolev embedding theorems and trace operator,
- test function and distribution spaces,
- analysis in distributions spaces (Fourier transform, differentiation, convolution),
- dual spaces of Sobolev spaces,
- fractional Sobolev spaces.
Sobolev Spaces (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-70-12-M-7||Sobolev Spaces||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||84 h||186 h||-||-||PL1||9.0||irreg.|
- About [MAT-70-12-K-7]: Title: "Sobolev Spaces"; Presence-Time: 84 h; Self-Study: 186 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 86405 ("Sobolev Spaces")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.
- H.-W. Alt: Lineare Funktionalanalysis,
- M. Dobrowolski: Angewandte Funktionalanalysis,
- M. Reed, B. Simon: Functional Analysis I.
Requirements for attendance (informal)
- [MAT-12-23-K-3] Introduction to Functional Analysis (2V+1U, 4.5 LP)
- [MAT-12-28-K-3] Measure and Integration Theory (2V+1U, 4.5 LP)