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 -