Functions with prescribed singularities
Giovanni Alberti, S. Baldo, G. Orlandi (2003)
Journal of the European Mathematical Society
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The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the...