Some boundary value problems elliptic in a subspace

In this paper we study a class of overdetermined systems of partial differential equations with constant coefficients which admit a special extension to elliptic systems. This extension allows us to pose boundary value problems for solutions of the original systems for which the corresponding operator is Noetherian as an operator to the space of right sides satisfying the necessary solvability conditions (ellipticity in a subspace). The system of equations of vector analysis or the system of Maxwell equations can serve as a model of the systems under consideration.
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