MATH 6130: Harnack Type Dirichlet Spaces (fall 2008)

Instructor: Laurent Saloff-Coste

This course will focus on the general notion of local Dirichlet form on locally compact spaces. We will discuss how a distance function can sometimes be attached to a Dirichlet form and the role played by the doubling volume condition and Poincaré inequalities in this setting. This will lead us to the definition of Harnack type Dirichlet spaces, and to the discussion of the properties of the weak solutions of the heat equation. Numerous concrete examples will be discussed.