Abstract

We prove that if p > 1, then the divergence of an L-p-vector field V on a 2-dimensional domain Omega is the boundary of an integral 1-current if and only if V can be represented as the rotated gradient del(perpendicular to)u for a W-1,W- p-map u : Omega -> S-1. Such a result extends to exponents p > 1 the result on distributional Jacobians of Alberti, Baldo, Orlandi (2003).