Prescribed singularities with weights
Résumé
We find the minimal weighted energy $\int\limits_\Omega a(x)|\mathrm{D}u|^n$ of maps \mbox{$u:\Omega\subset\mathbb{R}^{m+n}\to\mathbb{S}^n$} with prescribed singularities, where $a(\cdot)$ is a continuous positive weight. Our result extends previous ones of H.\,Brezis, J-M.\,Coron and E.H.\,Lieb (1986), G.\,Alberti, S.\,Baldo and G.\,Orlandi (2003), and V.\,Millot (2005).
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