Geodesic
Construction of polynomial solutions to the Dirichlet problem for the biharmonic equation in a ball
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 39-50

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Polynomial solution to the Dirihlet problem for the nonhomogeneous biharmonic equation with polynomial right hand side and polynomial boundary data in a ball is constructed. Explicit representation of harmonic functions in the Almansi representation is used.
Keywords: biharmonic equation, Dirichlet problem
Mots-clés : polynomial solutions, Almansi equation. 
@article{VYURM_2011_5_a5,
     author = {V. V. Karachik and N. A. Antropova},
     title = {Construction of polynomial solutions to the {Dirichlet} problem for the biharmonic equation in a ball},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {39--50},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2011_5_a5/}
}
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V. V. Karachik; N. A. Antropova. Construction of polynomial solutions to the Dirichlet problem for the biharmonic equation in a ball. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 39-50. http://geodesic.mathdoc.fr/item/VYURM_2011_5_a5/