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Modul
Introduction to Convex Integration [M-MATH-105964]
Credits
3Recurrence
UnregelmäßigDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-112119 | Introduction to Convex Integration | 3 |
Competence Certificate
The module will be completed with an oral exam (approx. 30 min).
Competence Goal
The main aim of this lecture is to introduce students to convex integration as a tool to construct solutions to partial differential equations.
In particular, they will be able to
- discuss the structure of convex integration algorithms,
- state major theorems and their relation,
- discuss regularity of convex integration solutions and uniqueness,
- discuss building blocks of constructions and their properties.
Prerequisites
none
Content
This lecture provides an introduction to the methods of convex integration and its applications:
- for isometric immersions,
- for the m-well problem in elasticity,
- for equations of fluid dynamics and
- higher regularity of convex integration solutions.
Recommendation
The modules "Classical Methods for Partial Differential Equations" and "Functional Analysis" are recommended.
Workload
Total workload: 90 hours
Attendance: 30 h
- lectures and examination
Self studies: 60 h
- follow-up and deepening of the course content,
- literature study and internet research on the course content,
- preparation for the module examination