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Scale-invariant Boundary Harnack Principle on Inner Uniform Domains in Fractal-type Spaces

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Abstract

We prove a scale-invariant boundary Harnack principle for inner uniform domains in metric measure Dirichlet spaces. We assume that the Dirichlet form is symmetric, strongly local, regular, and that the volume doubling property and two-sided sub-Gaussian heat kernel bounds are satisfied. We make no assumptions on the pseudo-metric induced by the Dirichlet form, hence the underlying space can be a fractal space.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, IL, 61801, USA

    Janna Lierl

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  1. Janna Lierl
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Correspondence to Janna Lierl.

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Initial stage of this research partially supported by NSF grant DMS 1004771.

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Lierl, J. Scale-invariant Boundary Harnack Principle on Inner Uniform Domains in Fractal-type Spaces. Potential Anal 43, 717–747 (2015). https://doi.org/10.1007/s11118-015-9494-1

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