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is used in France since 1951:

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http://www.bebe-prenoms.com/pages/prenom-yvelise-20258.html

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but, in Québec it is an ancient name attested by Jean-Claude Huriaux:

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http://cafe.rapidus.net/jhuriaux/femmesy.html

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Yvelise a combo of the root yv- (as in Yves or Yvain) and Élise.

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Here you can see a poster about this name:

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http://www.les-prenoms-en-bd.fr/drakkar.php?wpage=prenom.php%3Flibel%3DYvelise

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I don't know why Yvelise (and the misspellings Ivelise, Ivelisse, Yvelisse, Ivelis, etc.) is used in Puerto Rico and among othe Spanish speaking communities, but it seems another example of use of foreign names (often misspelled), known via films, books or tv-shows. Perhaps a character in a French film?

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Lumia
http://onomastica.mailcatala.com