Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes
Abstract
This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskii condition, elliptic estimates are established for functions supported near the boundary. The Fredholm property follows from additional hypotheses in the interior. This paper provides a rigorous framework for mode analysis on aAdS spacetimes for a wide range of boundary conditions considered in the physics literature. Completeness of eigenfunctions for some Bessel operator pencils is shown.
Keywords
Cite
@article{arxiv.1507.02794,
title = {Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes},
author = {Oran Gannot},
journal= {arXiv preprint arXiv:1507.02794},
year = {2018}
}
Comments
61 pages. Condensed and simplified following comments from the referee. To appear in Adv. Differential Equations