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Regularity Theory of Elliptic Partial Differential Equations
(dt. Regularitätstheorie elliptischer partieller Differentialgleichungen)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
One semester,
Person in charge of the module's outline Prof. Dr. Stephan Dahlke


  • 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.


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.

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 Wintersemester 2021/22. 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:

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.