On functions with a conjugate

Paul Baird; Michael Eastwood

doi:10.5802/aif.2931

On functions with a conjugate

Paul Baird, Michael Eastwood

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.

Original language	English
Pages (from-to)	277-314
Number of pages	38
Journal	Annales de l'Institut Fourier
Volume	65
Issue number	1
DOIs	https://doi.org/10.5802/aif.2931
Publication status	Published - 2015

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title = "On functions with a conjugate",

abstract = "Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.",

keywords = "3-harmonic function, Conformal Killing field, Conformal invariant, Conjugate function, Partial differential equation, Partial differential inequality",

author = "Paul Baird and Michael Eastwood",

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AU - Baird, Paul

AU - Eastwood, Michael

N1 - Publisher Copyright: © Association des Annales de l'institut Fourier, 2015, Certains droits réservés.

PY - 2015

Y1 - 2015

N2 - Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.

AB - Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.

KW - 3-harmonic function

KW - Conformal Killing field

KW - Conformal invariant

KW - Conjugate function

KW - Partial differential equation

KW - Partial differential inequality

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U2 - 10.5802/aif.2931

DO - 10.5802/aif.2931

M3 - Article

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VL - 65

SP - 277

EP - 314

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 1

ER -

On functions with a conjugate

Abstract

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