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Journal of Mathematical Sciences

, Volume 196, Issue 5, pp 721–732 | Cite as

Petrovskii elliptic systems in the extended Sobolev scale

  • Tetiana N. Zinchenko
  • Aleksandr A. Murach
Article

Abstract

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.

Keywords

Petrovskii elliptic system extended Sobolev scale Hörmander space RO-varying function interpolation with functional parameter a priori estimate of a solution local regularity of a solution 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Mathematics of the NAS of UkraineKievUkraine

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