## Lectures

### 2013/04/15

15:00-16:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Janna Lierl (University of Bonn)
Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)
[ Abstract ]
I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.
The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.
The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.
This is joint work with Laurent Saloff-Coste.