TY - JOUR

T1 - Polynomial growth solutions to higher-order linear elliptic equations and systems

AU - Chen, Roger

AU - Wang, Jiaping

PY - 2007/1

Y1 - 2007/1

N2 - 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 ℝn to ℝN, we prove that the dimension of the space of polynomial growth solutions of degree at most d is bounded by Cd2mnN, where C is a constant. If the system is in divergence form, we prove that this dimension is in fact bounded by CdmnN.

AB - 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 ℝn to ℝN, we prove that the dimension of the space of polynomial growth solutions of degree at most d is bounded by Cd2mnN, where C is a constant. If the system is in divergence form, we prove that this dimension is in fact bounded by CdmnN.

KW - Linear elliptic equation

KW - Linear elliptic system

KW - Polynomial growth solution

UR - http://www.scopus.com/inward/record.url?scp=70349647006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349647006&partnerID=8YFLogxK

U2 - 10.2140/pjm.2007.229.49

DO - 10.2140/pjm.2007.229.49

M3 - Article

AN - SCOPUS:70349647006

SN - 0030-8730

VL - 229

SP - 49

EP - 61

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -