Localization of a Helmholtz boundary value problem in a domain and the model problems

In the recent papers by A. Bonnet-Ben Dhia, L. Chesnel, P. Ciarlet, Jr, X. Claeys, M. Dauge and some others spectral properties of BVPs for the "anisotropic" Helmholtz equation with sign-different constants in two neighbouring domains were investigated with vanishing boundary conditions. They obtained sufficient conditions for the solvability by using some refinement of Lax-Milgram Lemma for T-coercive operators. In the present paper we describe the reduction of the problem to model problems.