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Graphs of $W^{1,1}$-maps with values in $S^{1}$: relaxed energies, minimal connections and lifting

Published online by Cambridge University Press:  18 September 2007

Mariano Giaquinta  and
Domenico Mucci
Mariano Giaquinta
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100 Pisa, Italy ([email protected])
Domenico Mucci
Affiliation:
Dipartimento di Matematica, Università di Parma, Viale G. P. Usberti 53/A, 43100 Parma, Italy ([email protected])
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Abstract

The aim of this paper is to link the analytic results of Brezis et al., Demengel and Ignat relative to $W^{1,1}$-mappings from $B^n$ into $S^1$ to the measure-theoretical geometric results in our previous work. The paper also contains a few remarks about mappings in $W^{1,p}$, $p\geq2$, with values in $S^2$.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 5 , October 2007 , pp. 937 - 962
Copyright
2007 Royal Society of Edinburgh

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