Inserted: 22 feb 2008
Last Updated: 26 may 2008
Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measure-valued solutions, under a quantitative Osgood condition on the velocity field. Our results extend those previously obtained for log-Lipschitz vector fields.
Keywords: currents, continuity equation, Osgood condition