The Hebrew University of Jerusalem
The Edmund Landau Minerva Center for Research in Mathematical
Analysis and Related Areas
THE LANDAU LECTURES 2008/2009
Professor Paul Rabinowitz (University of Wisconsin-Madison)
will deliver three lectures on:
IT ALL BEGAN WITH MOSER ...
- Thursday, December 18th and 22nd, 2008
- Towards an Aubry- Mather Theory for a class of PDE's
- In the late 1980's, Jürgen Moser initiated a PDE version of the work
of Aubry and of Mather for a class of dynamical systems. Moser was
interested in solutions possessing certain minimality and 'monotonicity'
properties. Over the past few years, there have been several extensions
of this work.
In the first lecture, a survey of this research will be presented.
In particular the application of minimization methods to find
certain basic solutions of the equations and the use of the basic
solutions to construct more complex solutions which undergo multiple
transitions will be described.
In the second lecture, we complete our
survey, take a closer look at some of the results, and discuss further types
- Wednesday, December 24th, 2008
- Variational gluing
- The multi-transition solutions mentioned in lectures 1-2 are
generally obtained by what may be called variational gluing arguments.
Minima of a functional are in a sense glued together to get new critical
points and new solutions of the associated Euler equation. In other
settings one deals with mountain pass critical points of a functional
rather than minima. In this lecture, we will discuss these matters and
also show how to construct hybrid solutions by gluing minimizers
and mountain pass solutions.
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Last updated: Oct. 28th, 2008
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