Эллиптические по Петровскому системы дифференциальных уравнений в уточненной шкале пространств на замкнутом многообразии

Abstract

We study a system of differential equations that is elliptic in the sense of Petrovskii on a closed compact smooth manifold. We prove that the operator generated by the system is a Fredholm one in a refined bilateral scale of functional Hilbert spaces. Elements of this scale are the isotropic spaces of Hörmander–Volevich–Paneyakh. An elliptic system with parameter is investigated as well.