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Existence of the Boundary Value of a Polyharmonic Function

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Abstract

We establish a criterion for existence of an L 2-limit and a weak L 2-limit of a polyharmonic function on a regular analytic boundary of a bounded plane domain.

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References

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Additional information

Original Russian Text Copyright © 2005 Mikhailov V. P.

The author was supported by the Russian Foundation for Basic Research (Grant 01-01-00988) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1542.2003.1).

In memory of Tadei Ivanovich Zelenyak.

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1125–1137, September– October, 2005.

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Mikhailov, V.P. Existence of the Boundary Value of a Polyharmonic Function. Sib Math J 46, 902–912 (2005). https://doi.org/10.1007/s11202-005-0087-x

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Keywords

  • polyharmonic equation
  • boundary value
  • compactness