On the Dirichlet problem for nonstrongly elliptic systems with nonconstant coefficients (Q1382868)

In a bounded three-dimensional domain the Dirichlet problem for a system of three special equations, elliptic in the Petrovskij sense, is considered. The equations depend on a numerical parameter. It is shown, that the Dirichlet problem is not of Noether type, as the parameter value is equal to 2. The proof is based on the Green's function method when the boundary value problem is reduced to a system of integral equations. This is for all parameter values \(\lambda\), except \(\lambda=2\), of Fredholm type. If this parameter is equal to 2, then one equation has not a Fredholm kernel and the Dirichlet problem is not of Noether type and has infinite deficiency indices.