Geodesic
On the mean value property for polyharmonic functions in the ball
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 69-88

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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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     author = {V. V. Karachik},
     title = {On the mean value property for polyharmonic functions in the ball},
     journal = {Matemati\v{c}eskie trudy},
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V. V. Karachik. On the mean value property for polyharmonic functions in the ball. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 69-88. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a4/