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Application of the almansi formula for constructing polynomial solutions to the dirichlet problem for a second-order equation

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Abstract

We obtain the Almansi decomposition for the second-order partial differential operators with constant coefficients. This decomposition is used for constructing a polynomial solution to the Dirichlet problem.

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Authors and Affiliations

  1. Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080, Russia

    V. V. Karachik

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  1. V. V. Karachik
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Correspondence to V. V. Karachik.

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Original Russian Text © V.V. Karachik, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 6, pp. 24–35.

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Karachik, V.V. Application of the almansi formula for constructing polynomial solutions to the dirichlet problem for a second-order equation. Russ Math. 56, 20–29 (2012). https://doi.org/10.3103/S1066369X12060035

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  • DOI: https://doi.org/10.3103/S1066369X12060035

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