A real analyticity result for symmetric functions of the eigenvalues of a domain dependent Neumann problem for the Laplace operator

Let Ω be an open connected subset of R^n for which the imbedding of the Sobolev space W^{1,2}(Ω) into the space L^2(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset φ(Ω) of R^n, where φ is a Lipschitz continuous homeomorphism of Ω onto φ(Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of φ.