Abstract
We are interested in the location of the singularities of maps u ∈ W s,p(S N, S 1) when 1 ≤ sp and 1 < sp < 2. To this end, we consider the distributional Jacobian. We show that the range of this operator on W s,p(S N, S 1) is the closure in W s−2,p ⋂ W −1,sp of the set of N − 2-currents defined as the integration on smooth oriented N − 2-dimensional boundaryless submanifolds.
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Bousquet, P. Topological singularities in W S,P (S N, S 1). J Anal Math 102, 311–346 (2007). https://doi.org/10.1007/s11854-007-0023-z
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DOI: https://doi.org/10.1007/s11854-007-0023-z