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Ukrainian Mathematical Journal

, Volume 66, Issue 7, pp 969–985 | Cite as

Regular Elliptic Boundary-Value Problems in the Extended Sobolev Scale

  • A. V. Anop
  • A. A. Murach
Article

We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean C - domain. It is shown that the operator of the problem is bounded and Fredholm in appropriate pairs of Hörmander inner-product spaces. They are parametrized with the help of an arbitrary radial function RO-varying at ∞ and form the extended Sobolev scale. We establish a priori estimates for the solutions of the problem and study their local regularity on this scale. New sufficient conditions for the generalized partial derivatives of the solutions to be continuous are obtained.

Keywords

Hilbert Space Sobolev Space Pseudodifferential Operator Interpolation Space Admissible Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. V. Anop
    • 1
  • A. A. Murach
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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