A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket

Q: What type of study is this?

This is a Quantitative Study study.

Yang Meng

doi:10.48550/arxiv.2505.04186

May 7, 2025Open Access

A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket

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Key Points

The direct proof establishes the cutoff Sobolev inequality, enhancing understanding of its mathematical significance.
Findings reveal a critical connection between Sobolev inequality and heat kernel estimates, improving theoretical foundations.
Approach involves rigorous mathematical techniques applied to the Sierpiński gasket, demonstrating key properties of the inequality.
This analysis highlights the complexity of the Sierpiński gasket, suggesting avenues for future research in fractal geometry.

Implication

Direct proof confirms the cutoff Sobolev inequality on the Sierpiński gasket, implying insights into heat kernel estimates.

Abstract

We present a direct proof of the cutoff Sobolev inequality on the Sierpiński gasket, which has long been regarded as highly non-trivial in the context of heat kernel estimates.

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Cite This Study

Yang Meng (2025) studied this question.

synapsesocial.com/papers/68e861a57ef2f04ca37e4590 https://doi.org/10.48550/arxiv.2505.04186

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A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket

Key Points

Implication

Abstract

Discussion

Cite This Study

A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket

Key Points

Implication

Abstract

Discussion

Cite This Study

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