Partial differential equations
Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes
Comptes Rendus. Mathématique, Volume 356 (2018) no. 10, pp. 988-1029.

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 Lopatinskiı̌ 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.

Cette Note considère des problèmes aux limites pour une classe d'opérateurs elliptiques singuliers, qui apparaissent naturellement dans l'étude des espaces-temps asymptotiquement anti-de Sitter (aAdS). Ces problèmes impliquent un opérateur de Bessel singulier agissant dans la direction normale. Après avoir formulé une condition de Lopatinskiı̌, nous établissons des estimations elliptiques pour les fonctions dont le support est voisin du bord. La propriété de Fredholm suit d'hypothèses additionnelles à l'intérieur. Nous fournissons ici un cadre rigoureux pour l'analyse des modes sur les espaces-temps aAdS d'une large classe de conditions au bord, considérées en physique. Nous montrons que certains pinceaux d'opérateurs de Bessel ont un ensemble complet de fonctions propres.

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DOI: 10.1016/j.crma.2018.08.003
Gannot, Oran 1

1 Department of Mathematics, Lunt Hall, Northwestern University, Evanston, IL 60208, USA
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Gannot, Oran. Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes. Comptes Rendus. Mathématique, Volume 356 (2018) no. 10, pp. 988-1029. doi : 10.1016/j.crma.2018.08.003. http://www.numdam.org/articles/10.1016/j.crma.2018.08.003/

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