Two remarks on liftings of maps with values into S1 |
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Authors: | Benoît Merlet |
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Institution: | LAGA, Institut Galilée, université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France |
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Abstract: | Given a map with some regularity: , we consider the problem of finding a lifting φ of u (i.e. a measurable function satisfying ) with the same regularity and with an optimal control . Two cases are treated here:(i) is a -seminorm, with and . We find a lifting φ such that and we show that the exponent cannot be improved.(ii) is the -seminorm where is a smooth open set. We give a simplified proof of a previous result J. Dàvila, R. Ignat, Lifting of BV functions with values in , C. R. Acad. Sci. Paris, Ser. I 337 (3) (2003) 159–164]: there exists satisfying . To cite this article: B. Merlet, C. R. Acad. Sci. Paris, Ser. I 343 (2006). |
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