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This entry is from Winter semester 2022/23 and might be obsolete. No current equivalent could be found.
Regularity Theory of Elliptic Partial Differential Equations
(dt. Regularitätstheorie elliptischer partieller Differentialgleichungen)
Level, degree of commitment | Specialization module, compulsory elective module |
Forms of teaching and learning, workload |
Lecture (3 SWS), recitation class (1 SWS), 180 hours (60 h attendance, 120 h private study) |
Credit points, formal requirements |
6 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination |
Language, Grading |
German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. |
Duration, frequency |
One semester, irregular |
Person in charge of the module's outline | Prof. Dr. Stephan Dahlke |
Contents
- Elliptic partial differential equations
- variational formulation
- function spaces
- Regularity of solutions in Sobolev and Besov spaces
Qualification Goals
The students shall
- recognise the relevance of regularity theory for practical problems, in particular for the numerical treatment of partial differential equations, and acquire knowledge of the basic principles of regularity estimations,
- learn how methods from functional analysis, numerical analysis and approximation theory interact,
- Re-evaluate knowledge from basic and advanced modules,
- to recognise the relations of regularity theory to other areas of mathematics and other sciences,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
Prerequisites
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Numerical Analysis.
Applicability
Module imported from M.Sc. Mathematics.
It can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- B.Sc. Business Mathematics
- M.Sc. Computer Science
- M.Sc. Mathematics
- M.Sc. Business Mathematics
When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.
The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.
Recommended Reading
- Theorie und Numerik elliptischer Differentialgleichungen, W. Hackbusch, Teubner Studienbücher (1996)
- Elliptic Boundary Value Problems in Domains with Point Singularities, V- Kozlov, V. Maz'ya und J. Rossmann, American Mathematical Society (1997)
- Elliptic Problems in Nonsmooth Domains, P. Grisvard, Pitman, Boston, (1985)
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24 (no corresponding element)
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.