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.
@article{urn:eudml:doc:41508,
title = {Gaussian estimates for fundamental solutions to certain parabolic systems.},
journal = {Publicacions Matem\`atiques},
volume = {48},
year = {2004},
pages = {481-496},
zbl = {1061.35023},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41508}
}
Hofmann, Steve; Kim, Seick. Gaussian estimates for fundamental solutions to certain parabolic systems.. Publicacions Matemàtiques, Tome 48 (2004) pp. 481-496. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41508/