Modul

The module will be completed by an oral exam (about 30 min).

The students

• can explain methods for definition of elliptic operators,
• can name results on spectral properties in L^q and relate them,
• can explain the relevance of heat kernel estimates and sketch corresponding methods of proof,
• can sketch the construction of the H^\infty calculus and name classes of elliptic operators for which it is bounded,
• can explain the concept of L^p maximal regularity and its relation to other parts of the theory and can name exmaples,
• have mastered the important techniques of proofs for regulariy properties of elliptic operators,
• are able to start a master thesis in the field.

none

• elliptic operators in divergence and non-divergence form
• elliptic operators on domains with boundary conditions
• heat kernel estimates for elliptic operators
• spectrum of elliptic operators in Lebesgue spaces L^q
• maximal L^p regularity for the parabolic problem
• H^\infty functional calculus for elliptic operators
• L^q theory for parabolic boundary value problems

The modules “Functional Analysis” and "Spectral Theory" are strongly recommended.

Total workload: 180 hours

Attendance: 60 h

• lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination