Monday Analysis Seminar: Potential analysis on nonsmooth domains

2011-5-30 14:45 - 2011-5-30 16:15
Faculty of Science Buliding #3 Room 210
Hiroaki Aikawa (Department of Mathematics, Hokkaido University)
Martin proved that every domain with Green function has the
Martin boundary which represents all positive harmonic
functions in the domain. The identification of the Martin
boundary is a very interesting question and attracts a lot
of attentions of numbers of mathematicians.

This talk is devoted to the Martin boundaries of nonsmooth
Euclidean domains and related subjects in potential theory.
Various interior and exterior conditions on domains are
presented with backgrounds. Observe that the boundary
Harnack principle and the Carleson estimate play important
roles for the identification of the Martin boundary.
If time allows, technical details such as Domar's argument
are touched.