This entry is from Summer semester 2018 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): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Modul Numerik (Numerische Basisverfahren) vermittelt werden.

## Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Mathematics
• M.Sc. Computer Science
• M.Sc. Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.

• 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)