MATS235 Sobolev Spaces (9 cr)
Learning outcomes
In the course, the basic properties of Sobolev spaces are studied. After the course, the student can use the definition of the weak derivative and its properties, Sobolev inequalities, approximation of Sobolev functions by smooth functions and different characterizations of Sobolev spaces.
Study methods
Course exam
Content
Sobolev spaces are an important tool in modern analysis and in applied mathematics. The course contain the essential parts of the theory of Sobolev spaces like
- the convolution approximation
- weak (distributional) derivatives
- partition of unity and approximation of Sobolev functions by smooth functions
- Sobolevin inequalities
- the ACL-charterization od Sobolev functions
- weak and strong convergence in L^p- and Sobolev spaces
- p-kapasiteetti
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| 9781482242386 | L.C. Evans & R.F. Gariepy, Measure Theory and Fine Properties of Functions |
| 978-0-387-97017-2 | W.P. Ziemer, Weakly Differentiable Functions |
| 978-0821847688 | G. Leoni, A first course in Sobolev spaces |
Prerequisites
Measure and integration theory 1&2