Abstract
We show that maps from Bn to a smooth compact boundaryless manifold which are smooth out of a singular set of dimension n−2 are dense for the strong topology in W1/2(Bn,). We also prove that for n≥2 smooth maps from Bn to are dense in W1/2(Bn,) if and only if π1()=0, i.e. the first homotopy group of is trivial.
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Giaquinta, M., Mucci, D. Density results for the W1/2 energy of maps into a manifold. Math. Z. 251, 535–549 (2005). https://doi.org/10.1007/s00209-005-0820-y
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DOI: https://doi.org/10.1007/s00209-005-0820-y