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arXiv · 1710.05716

Polynomial solutions of the boundary value problems for the Poisson equation in a layer

Oleg D. Algazin
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Abstract

In a multidimensional infinite layer bounded by two hyperplanes, the Poisson equation with the polynomial right-hand side is considered. It is shown that the Dirichlet boundary value problem and the mixed Dirichlet-Neumann boundary value problem with polynomial boundary conditions have a unique solution in the class of functions of polynomial growth and it solution is a polynomial. An algorithm for constructing this polynomial solution is given and examples are considered.

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Oleg D. Algazin. 2017-10-16. Polynomial solutions of the boundary value problems for the Poisson equation in a layer. https://arxiv.org/abs/1710.05716

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