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

Roger Chen, Jiaping Wang

Research output: Contribution to journalArticle

3 Scopus citations

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 (US)
Pages (from-to)49-61
Number of pages13
JournalPacific Journal of Mathematics
Volume229
Issue number1
DOIs
StatePublished - Jan 1 2007

Keywords

  • Linear elliptic equation
  • Linear elliptic system
  • Polynomial growth solution

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