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On Functions with a Conjugate

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Baird, Paul; Eastwood, Michael

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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.

dc.contributor.authorBaird, Paul
dc.contributor.authorEastwood, Michael
dc.date.accessioned2016-08-03T02:43:02Z
dc.date.available2016-08-03T02:43:02Z
dc.identifier.issn0373-0956
dc.identifier.urihttp://hdl.handle.net/1885/107111
dc.description.abstractHarmonic 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.
dc.description.sponsorshipThe first author is grateful for support provided by the Australian Research Council and to the Mathematical Sciences Institute at the Australian National University; part of this work was carried out under the award of a délégation auprès du CNRS. The second author is a Federation Fellow of the Australian Research Council and is grateful to the Département de Mathématiques á l’Université de Bretagne Occidentale for support and hospitality while working on this article.
dc.publisherAssociation des Annales de l'Institut Fourier
dc.rights© Association des Annales de l’institut Fourier, 2015. http://www.sherpa.ac.uk/romeo/issn/0373-0956/..."Publisher's version/PDF may be used. On author's personal website or institutional website or institutional server" from SHERPA/RoMEO site (as at 3/08/16).
dc.sourceAnnales de l'institut Fourier
dc.subjectconjugate function
dc.subjectconformal invariant
dc.subjectpartial differential inequality
dc.subjectpartial differential equation
dc.subject3-harmonic function
dc.subjectconformal Killing field
dc.titleOn Functions with a Conjugate
dc.typeJournal article
local.identifier.citationvolume65
dc.date.issued2015
local.publisher.urlhttp://aif.cedram.org/?lang=fr
local.type.statusPublished Version
local.contributor.affiliationEastwood, M., Mathematical Sciences Institute, The Australian National University
local.identifier.essn1777-5310
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage277
local.bibliographicCitation.lastpage314
local.identifier.doi10.5802/aif.2931
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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