Construction of Polynomial Solutions to Some Boundary Value Problems for Poisson's Equation

被引：24

作者：

Karachik, V. V. ^{[1
]}

机构：

[1] So Ural State Univ, Chelyabinsk 454080, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2011年 / 51卷 / 09期

关键词：

Almansi formula; polynomial solutions; Dirichlet problems for Poisson's equation; third boundary value problem for Poisson's equation;

D O I：

10.1134/S0965542511090120

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A polynomial solution of the inhomogeneous Dirichlet problem for Poisson's equation with a polynomial right-hand side is found. An explicit representation of the harmonic functions in the Almansi formula is used. The solvability of a generalized third boundary value problem for Poisson's equation is studied in the case when the value of a polynomial in normal derivatives is given on the boundary. A polynomial solution of the third boundary value problem for Poisson's equation with polynomial data is found.

引用

页码：1567 / 1587

页数：21

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