# Gaussian estimates for fundamental solutions to certain parabolic systems

@inproceedings{Hofmann2004GaussianEF,
title={Gaussian estimates for fundamental solutions to certain parabolic systems},
author={Stefan Hofmann and Seick Kim},
year={2004}
}
Abstract Auscher proved Gaussian upper bound estimates for the fundamental solutions to parabolic equations with complex coefficients in the case when coefficients are time-independent and a small perturbation of real coefficients. We prove the equivalence between the local boundedness property of solutions to a parabolic system and a Gaussian upper bound for its fundamental matrix. As a consequence, we extend Auscher’s result to the time dependent case.