On the solutions of the polynomic Laplacian equation

In this short communication we demonstrate a representation of the solutions of a partial differential equation, which is a polynomial in the Laplacian, in terms of harmonic functions alone. The idea is based on the Vekua Trasformation, which connects the kernel of the Laplace operator with the kern...

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Bibliographic Details
Published in:Quarterly of applied mathematics 2016-07, Vol.74 (4), p.643-646
Main Author: Dassios, George
Format: Article
Language:English
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Research article
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Summary:In this short communication we demonstrate a representation of the solutions of a partial differential equation, which is a polynomial in the Laplacian, in terms of harmonic functions alone. The idea is based on the Vekua Trasformation, which connects the kernel of the Laplace operator with the kernel of the Helmholtz operator. The representation can be applied to some well-known equations, such as the Brinkman equation in Viscous Hydrodynamics or the equation of Shells in Elasticity.
ISSN:0033-569X
1552-4485
DOI:10.1090/qam/1451