Modul

The module will be completed with an oral exam (approx. 30 min).

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.

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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.

The modules "Classical Methods for Partial Differential Equations" and "Functional Analysis" are recommended.

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