A new approach to two overdetermined eigenvalue problems of Pompeiu type

Free access article

Issue		ESAIM: Proc. Volume 2, 1997 Elasticity, viscoelasticity and optimal control


Page(s)		235 - 241
DOI		http://dx.doi.org/10.1051/proc:1997007

ESAIM: Proc., 1997, Vol. 2, pp. 235-241
DOI: 10.1051/proc:1997007

A new approach to two overdetermined eigenvalue problems of Pompeiu type

Thierry Chatelain

CNRS-Equipe de Mathématiques Université de Franche-Comté U 16, route de Gray 25030 Besançon, France

Abstract
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.

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