On p Laplace polynomial solutions

John L. Lewis, Andrew Vogel

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We determine all real homogeneous polynomial solutions to the p Laplace equation, - ∞< p< ∞, p≠ 1 , 2 , of degree four in Rn, n≥ 3 , and show there are no degree five real homogeneous polynomial solutions in R3, when - ∞< p< ∞, p≠ 1 , 2.

Original languageEnglish (US)
Pages (from-to)143-166
Number of pages24
JournalJournal of Analysis
Volume24
Issue number1
DOIs
StatePublished - Jun 2016

Keywords

  • p Harmonic functions
  • p Laplacian
  • Polynomial solutions
  • Real analytic

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics
  • Geometry and Topology

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