Geodesic
A new approach to two overdetermined eigenvalue problems of Pompeiu type
Thierry Chatelain1
1 CNRS-Equipe de Mathématiques Université de Franche-Comté U 16, route de Gray 25030 Besançon, France
ESAIM. Proceedings, Tome 2 (1997), pp. 235-241.

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We are interested in two overdetermined problems in spectral theory, known as Schiffer's conjectures and related to the Pompeiu problem. We show the connection between these problems and the critical points of the eigenvalue functional with a volume constraint. In two dimensions, we use this fact to establish an integral identity satisfied by a conformal map.
DOI : 10.1051/proc:1997007

Thierry Chatelain 1

1 CNRS-Equipe de Mathématiques Université de Franche-Comté U 16, route de Gray 25030 Besançon, France 
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Thierry Chatelain. A new approach to two overdetermined eigenvalue problems of Pompeiu type. ESAIM. Proceedings, Tome 2 (1997), pp. 235-241. doi : 10.1051/proc:1997007. http://geodesic.mathdoc.fr/articles/10.1051/proc:1997007/

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