Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces

Janna Lierl

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arXiv · 1201.2236

Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces

Janna Lierl

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Abstract

We prove a scale-invariant boundary Harnack principle for inner uni- form 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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BibTeX RIS

Janna Lierl. 2014-06-06. Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces. https://arxiv.org/abs/1201.2236

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