Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18671 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913625622446080 |
|---|---|
| author | Graves-McCleary, Anthony Saloff-Coste, Laurent |
| author_facet | Graves-McCleary, Anthony Saloff-Coste, Laurent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces Graves-McCleary, Anthony Saloff-Coste, Laurent Probability Analysis of PDEs 31C25 (Primary) 31E05 (Secondary) 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. |
| title | The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces |
| topic | Probability Analysis of PDEs 31C25 (Primary) 31E05 (Secondary) |
| url | https://arxiv.org/abs/2412.18671 |