JournalsrlmVol. 19, No. 3pp. 237–245

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

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Patrick Bernard

    Université de Paris Dauphine, France
Uniqueness of signed measures solving the continuity equation for Osgood vector fields cover

Abstract

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 two-sided Osgood condition on the velocity field. Our results extend those obtained for log-Lipschitz vector fields in \cite{BC}

Cite this article

Luigi Ambrosio, Patrick Bernard, Uniqueness of signed measures solving the continuity equation for Osgood vector fields. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 3, pp. 237–245

DOI 10.4171/RLM/522