Plenary Talk by Dr. Ludovic Dan Lemle

photo of Ludovic Dan Lemle

Location: Old Main Academic Building, Room 1030

Time: Sunday, May 8th, 8:30am - 9:30am

Webex Link

Title: On the Uniqueness of the Fokker-Planck-Kolmogorov Equation Associated with Schrödinger’s operators


Relating to a differential operator L, there are three important types of unique- ness:

(i)  the essential self-adjointness of L;

(ii)  the essential Markovian self-adjointness of L;

(iii)  uniqueness of weak solution of Martingale problem associated with L.

The starting point of my talk is represented by the uniqueness of the differential operators in the sense of the essential self-adjointness. In this context, we will introduce the essential generators on locally convex vector spaces and we will show that the next properties are equivalent:

(i)  L is an essential generator on L;

(ii)  the associated Cauchy problem has a L-unique strong solution;

(iii)  the associated Cauchy problem for the Fokker-Planck-Kolmogorov equation has a L1-unique weak solution.

So, there is a serious reason, of physical nature, for which this property of L to be an essential generator on L becomes very important because it is equivalent with the L1-uniqueness of the weak solution of the associated Cauchy problem for the Fokker-Planck-Kolmogorov equation.

In the second part of my talk, I will present the uniqueness of weak solution of the Cauchy problem for the Fokker-Planck-Kolomogorov equations associated with some Schrödinger’s type operators.