Analysis, Dynamics, and Applications Seminar

I will present a recent study on a class of ultraparabolic operators, that is, a Kolmogorov equation in which smoothing comes from a Hörmander condition.  We prove the existence of a fundamental solution and study its regularity under the relatively weak assumption that the equation's coefficients are Hölder continuous in space but merely bounded in time.  In particular, we adapt the classical parametrix technique of Levi in order to have a representation formula for the fundamental solution.  This is a joint work with Andrea Pascucci and Stefano Pagliarani.