On the Schrödinger heat kernel in horn-shaped domains
Volume 99 / 2004
Colloquium Mathematicum 99 (2004), 145-155
MSC: Primary 58J35; Secondary 35B40, 35B05, 47D06.
DOI: 10.4064/cm99-2-1
Abstract
We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.
