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