## Journal of the Mathematical Society of Japan

### 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 we do not assume volume doubling property for the symmetric measure.

#### Note

The first author was partially supported by NSERC (Canada). The second author was partially supported by NSERC (Canada) and the Pacific Institute for the Mathematical Sciences.

#### Article information

Source
J. Math. Soc. Japan, Volume 71, Number 2 (2019), 383-412.

Dates
Revised: 13 October 2017
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.jmsj/1551150260

Digital Object Identifier
doi:10.2969/jmsj/77057705

Mathematical Reviews number (MathSciNet)
MR3943443

Zentralblatt MATH identifier
07090048

#### Citation

BARLOW, Martin T.; MURUGAN, Mathav. Boundary Harnack principle and elliptic Harnack inequality. J. Math. Soc. Japan 71 (2019), no. 2, 383--412. doi:10.2969/jmsj/77057705. https://projecteuclid.org/euclid.jmsj/1551150260

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