Andrejewski-Tag: The H-principle - from Geometry to Physics

November 15, 2010

Program and lecture notes:

10:00 - 11:00 Lecture I: Y. Eliashberg, The h-principle and Gromovs convex integration

11:00 - 12:00 Exercise Session I

14:00 - 15:00 Lecture II: S. Müller, Differential Inclusions for Lipschitz mappings

15:00 - 16:00 Exercise Session II

17:00 - 18:00 Lecture III: L. Székelyhidi, Convex Integration and Turbulence

18:00 - 19:00 Exercise Session III

19:00 Party

Prerequisites:

• Notions from differential topology: manifolds, vector fields, differential forms; Ch.1 [1], Ch.4 [2]
• Elementary functional analysis: weak convergence, direct method, weak solutions; Ch.8.2 [3], Ch.11 [4]
• Basic real analysis: convolutions, almost everywhere differentiability, convexity; Ch.2 & 6 [4]

References:

• [1] Y. Eliashberg and N. Mishachev: Inroduction to the h-principle, AMS
• [2] V. Guillemin and A. Pollack: Differential Topology, Prentice-Hall
• [3] L. C. Evans: Partial Differential Equations, AMS
• [4] E. Lieb and M. Loss: Analysis, AMS
• [5] B. Kirchheim, S. Müller, V. Sverak: Studying nonlinear PDE by geometry in matrix space

The references are meant only as a guideline and contain much more information than required for the lectures.