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Improved scales of spaces and elliptic boundary-value problems. III

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Abstract

We study elliptic boundary-value problems in improved scales of functional Hilbert spaces on smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The local smoothness of a solution of an elliptic problem in an improved scale is investigated. We establish a sufficient condition under which this solution is classical. Elliptic boundary-value problems with parameter are also studied.

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Authors and Affiliations

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

    V. A. Mikhailets & A. A. Murach

  2. Chernigov Technological University, Chernigov

    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. 59, No. 5, pp. 679–701, May, 2007.

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Mikhailets, V.A., Murach, A.A. Improved scales of spaces and elliptic boundary-value problems. III. Ukr Math J 59, 744–765 (2007). https://doi.org/10.1007/s11253-007-0048-6

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  • DOI: https://doi.org/10.1007/s11253-007-0048-6

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