An integrability result for Lp-vector fields in the plane

摘要

We prove that if , then the divergence of an Lp-vector field V on a 2-dimensional domain is the boundary of an integral 1-current if and only if V can be represented as the rotated gradient for a W1,p-map . Such a result extends to exponents the result on distributional Jacobians of Alberti, Baldo, Orlandi (2003)