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arXiv · 2412.18671

The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces

Anthony Graves-McCleary·Laurent Saloff-Coste
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Abstract

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 Schr\"odinger operators.

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Anthony Graves-McCleary, Laurent Saloff-Coste. 2024-12-24. The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces. https://arxiv.org/abs/2412.18671

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