# Boundary Harnack principle and elliptic Harnack inequality

## TL;DR

This paper establishes a scale-invariant boundary Harnack principle for inner uniform domains in Dirichlet spaces, with robustness to time changes and without requiring volume doubling, advancing the understanding of elliptic inequalities.

## Contribution

It introduces a boundary Harnack principle applicable to a broad class of Dirichlet spaces, independent of volume doubling and stable under time changes.

## Key findings

- Proves scale-invariant boundary Harnack principle for inner uniform domains.
- Demonstrates robustness of assumptions under time changes of diffusions.
- Does not require volume doubling property for the symmetric measure.

## 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.