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

  • Mariano Giaquinta (a1) and Domenico Mucci (a2)


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 $S^2$.



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