Boundary expansion for the Loewner-Nirenberg problem in domains with conic singularities
Analysis of PDEs
2020-09-14 v3
Abstract
We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in domains with conic singularities and establish asymptotic expansions with respect to two normal directions simultaneously. 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. Key step is the study of the eigenvalues growth and eigenfunctions estimates.
Keywords
Cite
@article{arxiv.1806.07536,
title = {Boundary expansion for the Loewner-Nirenberg problem in domains with conic singularities},
author = {Xumin Jiang},
journal= {arXiv preprint arXiv:1806.07536},
year = {2020}
}