04-10-0518-vu Selected Topics in Analysis: Convex Integration

Lehrende: Prof. Ph.D. Stefano Modena

Veranstaltungsart: Vorlesung und Übung

Orga-Einheit: FB04 Mathematik

Anzeige im Stundenplan: Ausgew. Th. der Ana

Fach:

Anrechenbar für:

Semesterwochenstunden: 3

Unterrichtssprache: Deutsch und Englisch

Min. | Max. Teilnehmerzahl: - | -

Digitale Lehre:
Die Vorlesung und die Übung werden in Form eines Live-Streams mit Aufzeichnung stattfinden.

Lehrinhalte:
Convex integration is a technique for the construction of "strange" solutions to certain nonlinear systems of partial differential equations. The technique originates in the work of John Nash 1954 on C^1 isometric embeddings and has been developed into a powerful general method for certain problems in differential geometry and in the calculus of variations. In the last years new versions of this technique have been developed primarily for applications in fluid mechanics. The course aims to provide an introduction to some aspects of this theory.

Literatur:
L. Szekelyhidi, From isometric embeddings to turbulence, MPI lecture notes 41/2012.
C. De Lellis, L. Szekelyhidi, On admissibility criteria for weak solutions of the Euler equations, Arch. Rational Mech. Anal. 195 (2010), 225-260.
L. Szekelyhidi, Relaxation of the incompressible porous media equation, Annales scientifiques de l'École Normale Supérieure, Série 4, 45(3) (2012), 491-509

Voraussetzungen:
The course is suitable for master students and advances bachelor students.
 

Online-Angebote:
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