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 Dirichtet or Neumann boundary conditions, we show that the set of C-2k+1(Omega) perturbations of Omega, which preserves the multiplicity of the eigenvalue on the perturbed domain, is a manifold of codimension 2 in C-2k+1(Omega). (C) 1995 Academic Press, Inc.