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Petrovskii elliptic systems in the extended Sobolev scale

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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.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkivs’ka Str., Kiev, 01601, Ukraine

    Tetiana N. Zinchenko & Aleksandr A. Murach

Authors
  1. Tetiana N. Zinchenko
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  2. Aleksandr A. Murach
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Correspondence to Tetiana N. Zinchenko.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 10, No. 3, pp. 433–449, July–August, 2013.

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Zinchenko, T.N., Murach, A.A. Petrovskii elliptic systems in the extended Sobolev scale. J Math Sci 196, 721–732 (2014). https://doi.org/10.1007/s10958-014-1688-3

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  • DOI: https://doi.org/10.1007/s10958-014-1688-3

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