ON THE PERSISTENCE OF THE MULTIPLICITY OF EIGENVALUES FOR SOME VARIATIONAL ELLIPTIC OPERATOR DEPENDING ON THE DOMAIN

Given a bounded domain Omega subset of R(m) and an eigenvalue lambda( ) of multiplicity 2 for a variational elliptic operator L, with Dirich tet or Neumann boundary conditions, we show that the set of C-2k+1(Ome ga) perturbations of Omega, which preserves the multiplicity of the ei genvalue on the perturbed domain, is a manifold of codimension 2 in C- 2k+1(Omega). (C) 1995 Academic Press, Inc.