| 概要 | 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. |