Luigi Ambrosio

Transport Equation and Cauchy Problem for BV Vector Fields

Transport Equation and Cauchy Problem for BV Vector Fields

**ABSTRACT**. I will present some recent work and open problems on the
transport equation and the generic uniqueness of solutions of the ODE
in presence of a non-smooth vector field. The lectures will include the
classical theory of DiPerna-Lions as well as recent developments
concerning BV vector fields. Some applications to systems of
concervation laws and compactness of Lagrangian flows will
be presented. The main mathematical tools involved will be
the fine theory of BV functions and the theory of Young measures.