The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces
| Autor: | Graves-McCleary, Anthony, Saloff-Coste, Laurent |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 29 pages, 2 figures |
| Databáze: | arXiv |
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