Calculus of Variations and Geometric Measure Theory

L. Ambrosio - P. Bernard

Uniqueness of signed measures solving the continuity equation for Osgood vector fields

created by ambrosio on 22 Feb 2008
modified on 26 May 2008


Submitted Paper

Inserted: 22 feb 2008
Last Updated: 26 may 2008

Year: 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