On Functions with a Conjugate
[Sur les fonctions qui admettent une fonction conjuguée]
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 : https://doi.org/10.5802/aif.2931
Classification : 53A30
Mots clés : fonction conjuguée, invariant conforme, inégalité aux dérivées partielles, équation aux dérivées partielles, fonction 3-harmonique, champ de Killing conforme
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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://archive.numdam.org/articles/10.5802/aif.2931/

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