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arXiv · 2305.09292

Dirichlet forms on unconstrained Sierpinski carpets in $\mathbb{R}^3$

Shiping Cao·Hua Qiu
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Abstract

We prove the existence of a strongly local, regular, self-similar Dirichlet form with a sub-Gaussian heat kernel estimate on an unconstrained Sierpinski carpet in $\mathbb{R}^3$. In the setting under consideration, the walk dimension $d_W$ and the Hausdorff dimension $d_H$ always satisfy the inequality that $d_H>d_W$.

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Shiping Cao, Hua Qiu. 2023-05-16. Dirichlet forms on unconstrained Sierpinski carpets in $\mathbb{R}^3$. https://arxiv.org/abs/2305.09292

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