Journal of the Mathematical Society of Japan

Boundary Harnack principle and elliptic Harnack inequality

Martin T. BARLOW and Mathav MURUGAN

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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.


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

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

Received: 7 January 2017
Revised: 13 October 2017
First available in Project Euclid: 26 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31B25: Boundary behavior 31B05: Harmonic, subharmonic, superharmonic functions

boundary Harnack principle elliptic Harnack inequality


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.

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