### Abstract

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}.

Original language | English |
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Pages (from-to) | 49-61 |

Number of pages | 13 |

Journal | Pacific Journal of Mathematics |

Volume | 229 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*229*(1), 49-61. https://doi.org/10.2140/pjm.2007.229.49

}

*Pacific Journal of Mathematics*, vol. 229, no. 1, pp. 49-61. https://doi.org/10.2140/pjm.2007.229.49

**Polynomial growth solutions to higher-order linear elliptic equations and systems.** / Chen, Roger; Wang, Jiaping.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Chen, Roger

AU - Wang, Jiaping

PY - 2007/1/1

Y1 - 2007/1/1

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.

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

VL - 229

SP - 49

EP - 61

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -