Polynomial growth solutions to higher-order linear elliptic equations and systems

被引：0

作者：

Chen, Roger ^{[1
]}

Wang, Jiaping ^{[2
]}

机构：

[1] Natl Cheng Kung Univ, Dept Math, Tainan 701, Taiwan

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2007年 / 229卷 / 01期

关键词：

polynomial growth solution; linear elliptic equation; linear elliptic system;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an equation or system of equations Lu = 0, where L is a uniformly elliptic operator of order 2m and u is a map from R-n to R-N, we prove that the dimension of the space of polynomial growth solutions of degree at most d is bounded by Cd-2mnN, where C is a constant. If the system is in divergence form, we prove that this dimension is in fact bounded by Cd-mnN.

引用

页码：49 / 61

页数：13

共 7 条

[1] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].