论文标题
锥体中的洛恩 - 尼伦贝格问题
The Loewner-Nirenberg Problem in Cones
论文作者
论文摘要
我们研究有限锥中Loewner-Nirenberg问题解决方案的渐近行为，并根据无限锥中的相应溶液建立最佳的渐近扩张。允许形成锥体的球形域具有奇异性。在边界上具有奇异系数的这种球形域上的椭圆算子起着重要作用。由于球形域的奇异性，需要额外的护理来研究相关的奇异派问题的本征函数和解决方案的全球规则性。
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 boundary play an important role. Due to the singularity of the spherical domains, extra cares are needed for the study of the global regularity of the eigenfunctions and solutions of the associated singular Dirichlet problem.
