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Ukrainian Mathematical Journal

, Volume 64, Issue 4, pp 511–524 | Cite as

Neumann problem and one oblique-derivative problem for an improperly elliptic equation

  • V. P. Burskii
  • E. V. Lesina
Article
  • 49 Downloads

We study the problem of solvability of an inhomogeneous Neumann problem and an oblique-derivative problem for an improperly elliptic scalar differential equation with complex coefficients in a bounded domain. A model case in which the domain is a unit disk and the equation does not contain lower-order terms is investigated. It is shown that the classes of boundary data for which these problems are uniquely solvable in a Sobolev space are formed by the spaces of functions with exponentially decreasing Fourier coefficients.

Keywords

Elliptic Equation Unit Disk Dirichlet Problem Neumann Problem Pseudodifferential Operator 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. P. Burskii
    • 1
  • E. V. Lesina
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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