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.
Density results for the W^{1/2} energy of maps into a manifold / Giaquinta, M.; Mucci, Domenico. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 251:3(2005), pp. 535-549. [10.1007/s00209-005-0820-y]
Density results for the W^{1/2} energy of maps into a manifold
MUCCI, Domenico
2005
Abstract
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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