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Modul
Regularity for Elliptic Operators [M-MATH-106696]
Credits
6Recurrence
UnregelmäßigDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-113472 | Regularity for Elliptic Operators | 6 |
Competence Certificate
The module will be completed by an oral exam (about 30 min).
Competence Goal
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.
Prerequisites
none
Content
- 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
Recommendation
The modules “Functional Analysis” and "Spectral Theory" are strongly recommended.
Workload
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