ODE theory for nonsmooth vector fields, and applications

Prof. Dr. Luigi Ambrosio (SNS Pisa)

Abstract

In the lectures I will cover the theory of well-posedness for ODE's associated to nonsmooth vector fields, initiated by a seminal paper by DiPerna-Lions at the end of the 80's. This problem arises in many areas of Mathematical Physics, where the coupling between velocity and density (as for the semi-geostrophic equation, the Vlasov-Poisson equation, etc) rules out the possibility to apply the standard Cauchy- Lipschitz theory. I will cover particular classes of vector fields, as the Sobolev and BV ones, and I will also illustrate the quantitative side of this theory, mainly developed by G.Crippa and C.De Lellis. If time permits, I will also cover more recent developments of the theory in metric measure spaces, studied in a joint work with D.Trevisan.

Registration

No registration required.

Date and Place

All sessions take place in Seminar Room 02.06.011

• Tuesday, 09.05.2017:
  • 10:15 - 11:45 and 16:15 - 17:45

• Wednesday, 10.05.2017:
  • 11:30 - 13:00 and 16:15 - 17:45

• Thursday, 11.05.2017:
  • 10:15 - 11:45

-- DianeClaytonWinter - 21 Feb 2017