ON FUNCTIONS WITH A CONJUGATE

被引：2

作者：

Baird, Paul ^{[1
]}

Eastwood, Michael ^{[2
]}

机构：

[1] Univ Bretagne Occidentale, Lab Math Bretagne Atlantique, UMR 6205, 6 Av Victor Le Gorgeu,CS 93837, F-29238 Brest 3, France

[2] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia

来源：

ANNALES DE L INSTITUT FOURIER | 2015年 / 65卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

conjugate function; conformal invariant; partial differential inequality; partial differential equation; 3-harmonic function; conformal Killing field;

D O I：

10.5802/aif.2931

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：277 / 314

页数：38

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