Petrovskii elliptic systems in the extended Sobolev scale

TL;DR

This paper studies Petrovskii elliptic systems on smooth manifolds within the extended Sobolev scale, establishing solvability, a priori estimates, and regularity results for solutions in this generalized functional framework.

Contribution

It introduces the analysis of elliptic systems on the extended Sobolev scale, expanding classical results to a broader class of Hilbert spaces.

Findings

Proved theorems on solvability of elliptic systems in the extended Sobolev scale.

Established a priori estimates for solutions.

Analyzed the regularity properties of solutions.

Abstract

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.