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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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     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/

[1] V. V. Karachik, “Normalized system of functions with respect to the Laplace operator and its applications”, Journal of Mathematical Analysis and Applications, 287:2 (2003), 577–592 | DOI

[2] Karachik V. V., “On one representation of analytic functions by harmonic functions”, Siberian Advances in Mathematics, 18:2 (2008), 103–117 | DOI

[3] Karachik V. V., “On an expansion of Almansi type”, Mathematical Notes, 83:3–4 (2008), 335–344 | DOI | DOI

[4] N. Nicolescu, “Probléme de l'analyticité par rapport á un opérateur linéaire”, Studia Math., 16 (1958), 353–363

[5] Karachik V. V., “Almansi decompositions for non-singular second order partial differential operators”, Vestnik YuUrGU. Seriia «Matematika. Mehanika. Fizika», 30(206):3 (2010), 4–12 (in Russ.)

[6] Karachik V. V., Antropova N. A., “On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous Helmholtz equation”, Differential Equations, 46:3 (2010), 387–399

[7] Bondarenko B. A., Operator algorithms in differential equations, Fan, Tashkent, 1984, 183 pp.

[8] Karachik V. V., “Polynomial solutions to partial differential equations with constant coefficients, I”, Vestnik YuUrGU. Seriia «Matematika. Mehanika. Fizika», 10(227):4 (2011), 4–17 (in Russ.)

[9] Karachik V. V., “Construction of polynomial solutions to some boundary value problems for Poisson's equation”, Computational Mathematics and Mathematical Physics, 51:9 (2011), 1567–1587 | DOI