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Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1012–1021 | Cite as

On Boundary Values of Three-Harmonic Poisson Integral on the Boundary of a Unit Disk

  • S. B. Hembars’ka
Article
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Let C0 be a curve in a disk D = {|z| < 1} tangential to a circle at the point z = 1 and let Cθ be the result of rotation of this curve by an angle θ about the origin z = 0. We construct a bounded function u(z) three-harmonic in D with zero normal derivatives \( \frac{\partial u}{\partial n}\mathrm{and}\frac{\partial^2u}{\partial {r}^2} \) on the boundary such that the limit along Cθ does not exist for all θ, 0 ≤ θ ≤ 2π.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • S. B. Hembars’ka
    • 1
  1. 1.Lesya Ukrainka East-European National UniversityLuts’kUkraine

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