Sharp sub-Gaussian upper bounds for subsolutions of Trudinger’s equation on Riemannian manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-13 DOI:10.1016/j.na.2024.113641

Philipp Sürig

引用次数: 0

Abstract

We consider on Riemannian manifolds the nonlinear evolution equation $\partial_{t} u = Δ_{p} (u^{1 / (p - 1)}),$ where $p > 1$ . This equation is also known as a doubly non-linear parabolic equation or Trudinger’s equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including $R^{n}$ .

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黎曼流形上特鲁丁格方程子解的尖锐亚高斯上界

我们考虑了黎曼流形上的非线性演化方程∂tu=Δp(u1/(p-1))，其中 p>1. 该方程也称为双非线性抛物方程或特鲁丁格方程。我们证明该方程的弱子解具有亚高斯上界，并证明该上界对于包括 Rn 在内的某类流形是尖锐的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.