Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

I will present two-sided Gaussian bounds for the heat kernel corresponding to the Laplacian with a drift in certain Euclidean domains under Dirichlet boundary condition. These bounds will be derived for domains that are inner uniform. Inner uniformity is a condition on the boundary of the domain that is described solely in terms of the intrinsic length metric of the domain. Interesting examples of inner-uniform domains are the interior of the Koch snowflake and the complement of a convex set. In case the domain is bounded, our estimates imply the intrinsic ultracontractivity of the associated semigroup.

Speaker: Janna Lierl, Cornell University