MATS235 Sobolev Spaces (9 cr)
Study level:
Postgraduate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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
Completion methods
Course exam
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.
Description of prerequisites
Measure and integration theory 1&2
Literature
- L.C. Evans & R.F. Gariepy, Measure Theory and Fine Properties of Functions; ISBN: 9781482242386
- W.P. Ziemer, Weakly Differentiable Functions; ISBN: 978-0-387-97017-2
- G. Leoni, A first course in Sobolev spaces; ISBN: 978-0821847688
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
x
Teaching (9 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish