Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes

被引：3

作者：

Gannot, Oran ^{[1
]}

机构：

[1] Northwestern Univ, Dept Math, Lunt Hall, Evanston, IL 60208 USA

来源：

COMPTES RENDUS MATHEMATIQUE | 2018年 / 356卷 / 10期

关键词：

MASSIVE WAVE-EQUATION; QUASI-NORMAL MODES; GAUGED EXTENDED SUPERGRAVITY; BLACK-HOLES; SPACES; ADS; CURVATURE; STABILITY; RESOLVENT;

D O I：

10.1016/j.crma.2018.08.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers boundary value problems for a class of singular elliptic operators that 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. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：988 / 1029

页数：42

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