Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball

@article{Karachik2013PolynomialSO,
  title={Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball},
  author={V. Karachik and N. Antropova},
  journal={Differential Equations},
  year={2013},
  volume={49},
  pages={251-256}
}
We find a polynomial solution of the Dirichlet problem for the inhomogeneous biharmonic equation with polynomial right-hand side and polynomial boundary data in the unit ball. To this end, we use the closed-form representation of harmonic functions in the Almansi formula. 
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