Graduate Seminar
Conservation laws for fourth order systems in four dimensions
Tobias Lamm
28 Nov 2006, 17:00 – 19:00
In the first part of this talk I will briefly review the recent result of Tristan Riviere on the existence of a conservation law for weak solutions of the Euler-Lagrange equation of conformally invariant variational integrals in two dimensions. I will then show how we can adapt these arguments to show the existence of a conservation law for fourth order systems, including biharmonic maps into general target manifolds, in four dimensions. With the help of this conservation law I will then prove the continuity of weak solutions of these systems. If time permits I will also indicate how one can use this conservation law to prove the existence of a unique weak solution of the biharmonic map flow in the energy space.
This is a joint work with Tristan Riviere (ETH Zuerich).
http://geometricanalysis.mi.fu-berlin.de/os/os-ws0607.htm
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