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

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Ukrainian Mathematical Journal Aims and scope

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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Authors and Affiliations

  1. Lesya Ukrainka East-European National University, Luts’k, Ukraine

    S. B. Hembars’ka

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  1. S. B. Hembars’ka
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 7, pp. 876–884, July, 2018.

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Hembars’ka, S.B. On Boundary Values of Three-Harmonic Poisson Integral on the Boundary of a Unit Disk. Ukr Math J 70, 1012–1021 (2018). https://doi.org/10.1007/s11253-018-1548-2

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  • DOI: https://doi.org/10.1007/s11253-018-1548-2

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