热流的两重不等式和哈代-赫农抛物方程的可解性

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-25 DOI:arxiv-2407.17704

Yohei Tsutsui

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引用次数: 0

摘要

在本文中，我们通过应用稀疏支配，给出了整个空间上热流的两权重不等式。对于幂权，一些学者给出了这样的不等式。由于稀疏支配，我们可以处理 Muckenhoupt 类中的一般权重。作为应用，我们给出了Hardy-H\'enon抛物线方程的局部和全局存在性结果，该方程的势属于Muckenhoupt类。

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Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation

In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities were given by several authors. Owing to the sparse domination, we can treat general weights in Muckenhoupt classes. As a application, we present the local and global existence results for the Hardy-H\'enon parabolic equation, which has a potential belonging to a Muckenhoupt class.

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arXiv - MATH - Classical Analysis and ODEs

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