Geodesic
A~generalization of the Poisson integral formula for the functions harmonic and biharmonic in a~ball
Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 189-197

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We construct an analytic solution to the problem of extension to the unit $N$-dimensional ball of the potential on its values on an interior sphere. The formula generalizes the conventional Poisson formula. Bavrin's results obtained for the two-dimensional case by methods of function theory are transferred to the $N$-dimensional case ($N\ge3$). We also exhibit a solution to a similar extension problem for some operator expressions depending on a potential known on an interior sphere. A connection is established between solutions to the moment problem on a segment and on a semiaxis. 
@article{MT_2013_16_1_a9,
     author = {O. E. Yaremko},
     title = {A~generalization of the {Poisson} integral formula for the functions harmonic and biharmonic in a~ball},
     journal = {Matemati\v{c}eskie trudy},
     pages = {189--197},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2013_16_1_a9/}
}
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O. E. Yaremko. A~generalization of the Poisson integral formula for the functions harmonic and biharmonic in a~ball. Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 189-197. http://geodesic.mathdoc.fr/item/MT_2013_16_1_a9/