Boundary Harnack principle and elliptic Harnack inequality

Abstract

We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes of the corresponding diffusions. In particular, we do not assume volume doubling property for the symmetric measure.

31 pages, 1 figure; incorporated referee comments; to appear in Journal of the Mathematical Society of Japan