On Functions with a Conjugate
[Sur les fonctions qui admettent une fonction conjuguée]
Baird, Paul1 ; Eastwood, Michael2
1 Laboratoire de Mathématiques de Bretagne Atlantique UMR 6205 Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 Brest Cedex 3 (France)
2 Mathematical Sciences Institute Australian National University, ACT 0200 (Australia)
Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 277-314.

Les fonctions harmoniques en deux variables sont exactement celles qui admettent une fonction conjuguée, à savoir une fonction dont le gradient a la même longueur et est partout orthogonal au gradient de la fonction d’origine. Nous montrons qu’il existe des équations aux dérivées partielles qui contrôlent également les fonctions de trois variables qui admettent une fonction conjuguée.

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.

DOI : 10.5802/aif.2931
Classification : 53A30
Keywords: conjugate function, conformal invariant, partial differential inequality, partial differential equation, 3-harmonic function, conformal Killing field
Mot clés : fonction conjuguée, invariant conforme, inégalité aux dérivées partielles, équation aux dérivées partielles, fonction 3-harmonique, champ de Killing conforme
Baird, Paul 1 ; Eastwood, Michael 2

1 Laboratoire de Mathématiques de Bretagne Atlantique UMR 6205 Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 Brest Cedex 3 (France)
2 Mathematical Sciences Institute Australian National University, ACT 0200 (Australia) 
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Baird, Paul; Eastwood, Michael. On Functions with a Conjugate. Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 277-314. doi : 10.5802/aif.2931. http://www.numdam.org/articles/10.5802/aif.2931/

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