On completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary
[Sur la complétude des fonctions propres et associées d'un problème au bord elliptique dans un domaine avec points coniques sur le bord]
Egorov, Youri V.1 ; Kondratiev, Vladimir A.2 ; Schulze, Bert-Wolfgang3
1 Laboratoire des mathématiques pour l'industrie et la physique, UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31062, Toulouse cedex 4, France
2 Mehmat Faculty, Lomonosov University, Vorob'evy Gory, 119899 Moscow, Russia
3 Institute of Mathematics, Potsdam University, 601553 Potsdam, Germany
Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 649-654.

On montre que les fonctions propres et associées d'un problème au bord pour un opérateur elliptique d'ordre 2m, défini dans un domaine dans ℝ n avec points coniques sur le bord, forment un système total.

We prove the completeness of the system of eigen and associated functions (i.e., root functions) of an elliptic boundary value problem in a domain, whose boundary is a smooth surface everywhere, except at a finite number of points, such that each point possesses a neighborhood, where the boundary is a conical surface.

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DOI : 10.1016/S1631-073X(02)02320-8
Egorov, Youri V. 1 ; Kondratiev, Vladimir A. 2 ; Schulze, Bert-Wolfgang 3

1 Laboratoire des mathématiques pour l'industrie et la physique, UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31062, Toulouse cedex 4, France
2 Mehmat Faculty, Lomonosov University, Vorob'evy Gory, 119899 Moscow, Russia
3 Institute of Mathematics, Potsdam University, 601553 Potsdam, Germany 
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     title = {On completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary},
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Egorov, Youri V.; Kondratiev, Vladimir A.; Schulze, Bert-Wolfgang. On completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 649-654. doi : 10.1016/S1631-073X(02)02320-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02320-8/

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