锥体中的洛伊文纳-尼伦堡问题

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-07-04 DOI:10.1016/j.jfa.2024.110566

Qing Han , Xumin Jiang , Weiming Shen

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引用次数: 0

摘要

我们研究了有限锥体中 Loewner-Nirenberg 问题解的渐近行为，并根据无限锥体中的相应解建立了最优渐近展开。形成圆锥的球面域允许存在奇点。这种球形域上的椭圆算子在边界上的奇异系数起着重要作用。由于球面域的奇异性，在研究相关奇异 Dirichlet 问题的特征函数和解的全局正则性时需要格外小心。

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The Loewner-Nirenberg problem in cones

We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in finite cones and establish optimal asymptotic expansions in terms of the corresponding solutions in infinite cones. The spherical domains over which cones are formed are allowed to have singularities. An elliptic operator on such spherical domains with coefficients singular on the boundary plays an important role. Due to the singularity of the spherical domains, extra care is needed for the study of the global regularity of the eigenfunctions and solutions of the associated singular Dirichlet problem.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis