Tatiana Toro
University of Washington
In this talk we would like to convey the idea that there is a
strong relationship between the geometry of the boundary of a domain in
Euclidean space and the boundary regularity of the solutions to Laplace's
equation. In particular we will show that the doubling properties of the
harmonic measure and the "regularity" of the Poisson kernel of a domain
in Euclidean space characterize the geometry and the "smoothness"
of the boundary of
. We introduce some new notions of regularity
which are well adapted to study domains whose boundaries are not smooth
enough to fit into the classical scheme.