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Elliptic Operators in a Refined Scale of Functional Spaces

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Abstract

We study the theory of elliptic boundary-value problems in a refined two-sided scale of the Hormander spaces H s, ϕ, where s ∈ R and ϕ is a functional parameter slowly varying at +∞. For the Sobolev spaces H s, the function ϕ(|ξ|) ≡ 1. We establish that the considered operators possess the Fredholm property, and solutions are globally and locally regular.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    V. A. Mikhailets

  2. Chernigov Technological Institute, Chernigov, Ukraine

    A. A. Murach

Authors
  1. V. A. Mikhailets
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  2. A. A. Murach
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 689–696, May, 2005.

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Mikhailets, V.A., Murach, A.A. Elliptic Operators in a Refined Scale of Functional Spaces. Ukr Math J 57, 817–825 (2005). https://doi.org/10.1007/s11253-005-0231-6

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  • DOI: https://doi.org/10.1007/s11253-005-0231-6

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