The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces Article Swipe
Anthony Graves‐McCleary
,
Laurent Saloff‐Coste
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.18671
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.18671
We prove a generalized version of the $3G$ Principle for Green's functions on bounded inner uniform domains in a wide class of Dirichlet spaces. In particular, our results apply to higher-dimensional fractals such as Sierpinski carpets in $\mathbf{R}^n$, $n\geq 3$, as well as generalized fractal-type spaces that do not have a well-defined Hausdorff dimension or walk dimension. This yields new instances of the $3G$ Principle for these spaces. We also discuss applications to Schrödinger operators.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2412.18671
- https://arxiv.org/pdf/2412.18671
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4405904600
All OpenAlex metadata
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https://openalex.org/W4405904600Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2412.18671Digital Object Identifier
- Title
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The Boundary Harnack Principle and the 3G Principle in Fractal-Type SpacesWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-12-24Full publication date if available
- Authors
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Anthony Graves‐McCleary, Laurent Saloff‐CosteList of authors in order
- Landing page
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https://arxiv.org/abs/2412.18671Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2412.18671Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2412.18671Direct OA link when available
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Harnack's principle, Fractal, Harnack's inequality, Type (biology), Boundary (topology), Mathematics, Mathematical analysis, Pure mathematics, Geology, PaleontologyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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