On variational formulations of inner boundary value problems for infinite systems of elliptic equations of special kind

We consider boundary value problems for infinite triangular systems of elliptic equations with variable coefficients in 3d Lipschitz domains. Variational formulations of Dirichlet, Neumann and Robin problems are received and their well posedness in corresponding Sobolev spaces is established. With the help of introduced q-convolution the integral representations of generalized solutions of formulated problems in the case of constant coefficients are built. We investigate the properties of integral operators and well posedness of received systems of boundary integral equations.