Special Session 60: 

On free boundary problems for conformally invariant variational functions

Armin Schikorra
U Pittsburgh
USA
Co-Author(s):    
Abstract:
I will present a regularity result at the free boundary for critical points of a large class of conformally invariant variational functionals. The main argument is that the Euler-Lagrange equation can be interpreted as a coupled system, one of local nature and one of nonlocal nature, and that both systems (and their coupling) exhibit an antisymmetric structure which leads to regularity estimates.