This article is cited in 12 papers

On polynomial solutions to the Dirichlet problem for a biharmonic equation in a ball

V. V. Karachik, N. A. Antropova

South Ural State University, Chelyabinsk, Russia

Abstract: 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, polynomial solutions, Almansi formula.

UDC: 517.956.225+517.575

Received: 08.07.2011

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