Non-Linear Partial Differential Equations and Sobolev Spaces

The course gives an introduction to mathematical methods and structures that are fundamental for the study of partial differential equations, calculus of variations, etc. Furthermore, the course is useful for a rigorous understanding of numerical analysis. The following topics are covered: Distribution theory, Sobolov spaces, functional analysis, compactness arguments, and error estimates. Selected topics.

1. Knowledge. The course covers basic methods and structures fundamental for the study of partial differential equations, calculus of variations, etc. Furthermore, the course is useful for a rigorous understanding of numerical analysis. The following topics are covered: Distribution theory, Sobolev spaces, functional analysis, compactness arguments, and error estimates. 2. Skills. The students are familiar with the theory of distributions and Sobolev spaces and able to use these techniques in various problems in differential equations, functional analysis and applied disciplines. 3. Competence. The students should be able to participate in scientific discussions and conduct researches on high international level in the theory of distributions and Sobolev spaces and their applications to various areas of Mathematics.

Lectures, possibly guided self-study.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.