Mathematics - Colloquium
Friday, October 9, 2009
11:00 AM-12:00 PM
TITLE: On the global regularity of conformal maps
ABSTRACT: The Riemann mapping theorem, one of the most celebrated results in complex analysis, states that any bounded, connected and simply connected domain $D$ in ${\Bbb R}^2$ can be conformally mapped onto the unit disk. It has long been understood that there are subtle connections between the smoothness of the conformal transformation $\Phi$ near the boundary of the domain and the degree of regularity of $D$. In this talk we address the issue of global regularity of $\Phi$ on Sobolev-Besov scales, in the case when the domain $D$ is allowed to have a Lipschitz graph-like boundary. The approach employed relies on powerful tools from Harmonic Analysis and PDE's, in particular on boundary layer potentials and sharp estimates for the solution of the Dirichlet Laplacian with Besov data in Lipschitz domains.
Suggested Audiences: Adult, College
E-mail:
ma-chair@wpi.edu
Last Modified: October 5, 2009 at 1:06 PM