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Tangential limit values of a biharmonic poisson integral in a disk

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Abstract

Let C 0 be a curve in a disk D={|z|<1} that is tangent to the circle at the point z=1, and let C θ be the result of rotation of this curve about the origin z=0 by an angle θ. We construct a bounded function biharmonic in D that has a zero normal derivative on the boundary and for which the limit along C θ does not exist for all θ, 0≤θ≤2π.

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Authors
  1. S. B. Hembars'ka
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Additional information

Volyn University, Lutsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1171–1176, September, 1997.

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Hembars'ka, S.B. Tangential limit values of a biharmonic poisson integral in a disk. Ukr Math J 49, 1317–1323 (1997). https://doi.org/10.1007/BF02487338

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  • DOI: https://doi.org/10.1007/BF02487338

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