Calculus of Variations and Geometric Measure Theory
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G. Alberti - S. Baldo - G. Orlandi

Functions with prescribed singularities

created on 23 Jan 2003
modified by alberti on 06 Mar 2007


Published Paper

Inserted: 23 jan 2003
Last Updated: 6 mar 2007

Journal: J. Eur. Math. Soc.
Volume: 5
Number: 3
Pages: 275-311
Year: 2003

Final version, April 2003


The distributional k-dimensional Jacobian of a Sobolev map u which takes values in the (k-1)-dimensional sphere can be viewed as a rectifiable current of codimension k located on (a part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator. We show that any boundary M of codimension k can be realized as Jacobian of a Sobolev map; and in case M is polyhedral, the map we construct is smooth outside M plus an additional polyhedral set of lower dimension.

Keywords: Rectifiability, coarea formula, distributional jacobian, integral currents, singular maps


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