Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.10.005

Tianling Jin , Jingang Xiong

引用次数: 33

Abstract

We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated theorem of Caffarelli-Gidas-Spruck for the second order Yamabe equation with isolated singularities to higher order equations. Our approach uses blow up analysis for local integral equations, and is unified for all critical elliptic equations of order smaller than the dimension. We also prove the existence of Fowler solutions to the global equations, and establish a sup ⁎ inf type Harnack inequality of Schoen for integral equations.

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具有孤立奇点的高阶共形不变方程解的渐近对称性和局部性质

证明了具有孤立奇点的高阶共形不变方程在有界区域上解的急剧爆破率，并证明了其解在奇点附近的渐近径向对称性。这是关于二阶孤立奇点的Yamabe方程的著名的Caffarelli-Gidas-Spruck定理对高阶方程的推广。该方法对局部积分方程采用爆破分析，对所有小于维数的临界椭圆方程统一。我们还证明了整体方程的Fowler解的存在性，并建立了积分方程的一个sup  inf型harack不等式。

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.