Differentiability properties of the flow associated with rough vector fields


Friday, September 13th 12:00 – 12:25, 2019
WASTE4T Room at DeustoTech

Nicola De Nitti
Università degli Studi di Bari Aldo Moro

Abstract:

The classical Cauchy-Lipschitz theorem guarantees existence, uniqueness, and Lipschitz regularity (with respect to the initial datum) of the flow associated with a Lipschitz continuous vector field. In the last few decades – in view of possible applications to fluid dynamics and to the theory of conservation laws – much effort has been put into the study of ODEs driven by vector fields which are not necessarily Lipschitz continuous, but belong only to some class of weak differentiability. The aim of this talk is to present some recent regularity results for the flow associated with a BV vector field