Geodesic
On polynomial solutions to the Dirichlet problem for a~biharmonic equation in a~ball
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 2, pp. 86-98

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We find a polynomial solution to the Dirichlet problem for an inhomogeneous biharmonic equation with polynomial right-hand side and polynomial boundary data in the unit ball. We use an explicit representation of harmonic functions in the Almansi formula.
Keywords: biharmonic equation, harmonic polynomials, Dirichlet problem
Mots-clés : polynomial solutions, Almansi formula. 
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     author = {V. V. Karachik and N. A. Antropova},
     title = {On polynomial solutions to the {Dirichlet} problem for a~biharmonic equation in a~ball},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {86--98},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a8/}
}
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V. V. Karachik; N. A. Antropova. On polynomial solutions to the Dirichlet problem for a~biharmonic equation in a~ball. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 2, pp. 86-98. http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a8/