On p Laplace polynomial solutions

John L. Lewis; Andrew Vogel

doi:10.1007/s41478-016-0005-6

On p Laplace polynomial solutions

John L. Lewis, Andrew Vogel

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	143-166
Number of pages	24
Journal	Journal of Analysis
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s41478-016-0005-6
State	Published - Jun 2016

Keywords

Polynomial solutions
Real analytic
p Harmonic functions
p Laplacian

ASJC Scopus subject areas

Algebra and Number Theory
Analysis
Applied Mathematics
Geometry and Topology

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10.1007/s41478-016-0005-6

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title = "On p Laplace polynomial solutions",

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.",

keywords = "Polynomial solutions, Real analytic, p Harmonic functions, p Laplacian",

author = "Lewis, {John L.} and Andrew Vogel",

note = "Publisher Copyright: {\textcopyright} 2016, Forum D' Analystes, Chennai.",

year = "2016",

month = jun,

doi = "10.1007/s41478-016-0005-6",

language = "English (US)",

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AU - Vogel, Andrew

PY - 2016/6

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N2 - 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.

AB - 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.

KW - Polynomial solutions

KW - Real analytic

KW - p Harmonic functions

KW - p Laplacian

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JO - Journal of Analysis

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On p Laplace polynomial solutions

Abstract

Keywords

ASJC Scopus subject areas

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