We show that maps from Bn to a smooth compact boundaryless manifold Y which are smooth out of a singular set of dimension n−2 are dense for the strong topology in W1/2(Bn,Y). We also prove that for n ≥ 2 smooth maps from Bn to Y are dense in W1/2(Bn,Y) if and only if π_1(Y) = 0, i.e. the first homotopy group of Y is trivial.
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