A new approach to two overdetermined eigenvalue problems of Pompeiu type
CNRS-Equipe de Mathématiques Université de Franche-Comté U 16, route de Gray 25030 Besançon, France
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.
© EDP Sciences, ESAIM, 1997