Uniform approximation of functions by polynomial solutions to second-order elliptic equations on compact sets in R2

被引：2

作者：

Zaitsev, AB ^{[1
]}

机构：

[1] Moscow Inst Radio Engn Elect & Automat, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2003年 / 74卷 / 1-2期

关键词：

uniform approximability; second-order homogeneous elliptic equation with constant coefficients; strongly elliptic operator; Caratheodory domain;

D O I：

10.1023/A:1025010914890

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study necessary and sufficient conditions for functions to be approximated uniformly on plane compact sets by polynomial solutions to second-order homogeneous elliptic equations with constant coefficients. Sufficient conditions for approximability are of reductive character, i.e., the possibility of approximating on some (simpler) parts of the compact set implies approximability on the entire compact set.

引用

页码：38 / 48

页数：11

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