On Overdetermined Eigenvalue Problems for the Polyharmonic Operator

Robert Dalmasso (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

We consider two eigenvalue problems for the polyharmonic operator, with overdetermined boundary conditions. We give an equivalent integral formulation. In some cases we obtain characterizations of open balls by means of integral identities.

Mots clés: polyharmonic operator; overdetermined problems

Domaines: Equations aux dérivées partielles [math.AP]

Robert Dalmasso. On Overdetermined Eigenvalue Problems for the Polyharmonic Operator. Journal of Mathematical Analysis and Applications, 1998, 221 (1), pp.384-404. ⟨10.1006/jmaa.1997.5906⟩. ⟨hal-00387616⟩