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

Roger Chen, Jiaping Wang

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)49-61
Number of pages13
JournalPacific Journal of Mathematics
Volume229
Issue number1
DOIs
Publication statusPublished - 2007 Jan 1

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Polynomial Growth
Elliptic Systems
Elliptic Equations
Linear equation
Linear Systems
Higher Order
Elliptic Operator
System of equations
Divergence
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Pacific Journal of Mathematics, Vol. 229, No. 1, 01.01.2007, p. 49-61.

Research output: Contribution to journalArticle

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