Polynomial solutions of the boundary value problems for the Poisson equation in a layer
Mathematical Physics
2017-10-17 v1 Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1710.05716,
title = {Polynomial solutions of the boundary value problems for the Poisson equation in a layer},
author = {Oleg D. Algazin},
journal= {arXiv preprint arXiv:1710.05716},
year = {2017}
}