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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-2-1,
author = {Gabriele Grillo},
title = {On the Schr\"odinger heat kernel in horn-shaped domains},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {145-155},
zbl = {1052.58028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-2-1}
}
Gabriele Grillo. On the Schrödinger heat kernel in horn-shaped domains. Colloquium Mathematicae, Tome 100 (2004) pp. 145-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-2-1/