Potential theory
with applications to elliptic (and subelliptic) PDEs

The aim of this course is to present a potential theory which applies to a large class of elliptic and subelliptic operators L. The course will consist essentially of two parts. The first part will include basic properties of superharmonic functions, the Riesz decomposition, the resolvent equation, existence of the global Green function and the general theory of the Martin boundary (which is a natural compactification of a domain, in terms of the operator L)

The second part is connected to some fairly recent results. We are going to apply the potential theoretic approach to the elliptic (or subelliptic) operators L on unbounded domains D and having the property that for an eps>0, L + eps I admits a Green function on D. This gives a description of positive L-harmonic functions on D and some estimates of them as well.

First meeting

The first meeting will be devoted to an introductory lecture which is supposed to give a better idea of what the course is going to include.

Wednesday, February 7, 10:15-12:00 in S1

Ewa Damek <edamek@math.chalmers.se>

Last modified February 1, 1996, by Lars Alexandersson <larsa@math.chalmers.se>