Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains

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This is a Quantitative Study study.

Riku Anttila

doi:10.48550/arxiv.2510.04725

October 6, 2025Open Access

Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains

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Key Points

Sub-gaussian heat kernel estimates are applicable to the reflected diffusion process on inner uniform domains, indicating a significant extension of previous theories.
This research establishes that sub-gaussian estimates from ambient spaces can be inherited by the reflected diffusion processes, enhancing our understanding of diffusion behavior.
The methods used in this analysis focus on diffusion processes within specific geometrical constraints, particularly emphasizing inner uniform domains.
This work lays the groundwork for potential applications in mathematical models involving reflections and diffusion processes in diverse fields.

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Implication

New findings show reflected diffusion maintains sub-gaussian heat kernel estimates in inner uniform domains, suggesting broader applications.

Abstract

We prove that sub-Gaussian heat kernel estimates are inherited from a diffusion process on the ambient space to the reflected diffusion process on a subset which is an inner uniform domain.

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Cite This Study

Riku Anttila (2025) studied this question.

synapsesocial.com/papers/68e997abe14057276da7f1f7 https://doi.org/10.48550/arxiv.2510.04725

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Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains

Key Points

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Implication

Abstract

Discussion

Cite This Study

Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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