Abstract: We define the Dirichlet to Neumann Operator by form methods on
arbitrary Lipschitz domains. This is done with the help of a weak
definition of the normal derivative. The Dirichlet to Neumann Operator is
a selfadjoint operator with compact resolvent. Its spectrum is closely
related to the spectra of the Laplacian with Robin boundary conditions.
Among diverse interesting spectral properties we obtain a result by
Friedlander from 1992 which says that the (n+1)-th eigenvalue of the
Neumann Laplacian is smaller or equal than the n-th eigenvalue of the
Dirichlet Laplacian.