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On the mean value property for polyharmonic functions in the ball

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Abstract

We obtain the mean value property for the normal derivatives of a polyharmonic function with respect to the unit sphere. We find the values of a polyharmonic function and its Laplacians at the center of the unit ball expressed via the integrals of the normal derivatives of this function over the unit sphere.

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Authors and Affiliations

  1. South Ural State University, Chelyabinsk, 454080, Russia

    V. V. Karachik

Authors
  1. V. V. Karachik
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Correspondence to V. V. Karachik.

Additional information

Original Russian Text © V. V. Karachik, 2013, published in Matematicheskie Trudy, 2013, Vol. 16, No. 2, pp. 69–88.

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Karachik, V.V. On the mean value property for polyharmonic functions in the ball. Sib. Adv. Math. 24, 169–182 (2014). https://doi.org/10.3103/S1055134414030031

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  • DOI: https://doi.org/10.3103/S1055134414030031

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