Petrovskii elliptic systems in the extended Sobolev scale

Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated in the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. Theorems of solvability of the elliptic systems in the extended Sobolev scale are proved. An a priori estimate for solutions is obtained, and their local regularity is studied.