Geodesic
Integral identities on a sphere for normal derivatives of polyharmonic functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 533-551

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Identities for the integrals over the unit sphere of the products of linear combinations of normal derivatives of polyharmonic function in the unit ball and homogeneous harmonic polynomials are obtained. Basing on these identities the necessary conditions for the values on the unit sphere of polynomials on normal derivatives of polyharmonic functions are derived. Illustrative examples are given.
Keywords: polyharmonic functions, higher order normal derivatives, integral identities on the sphere. 
@article{SEMR_2017_14_a116,
     author = {V. V. Karachik},
     title = {Integral identities on a sphere for normal derivatives of polyharmonic functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {533--551},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a116/}
}
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V. V. Karachik. Integral identities on a sphere for normal derivatives of polyharmonic functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 533-551. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a116/