Gaussian estimates for fundamental solutions to certain parabolic systems.
Publicacions Matemàtiques, Tome 48 (2004) no. 2, p. 481-496.
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.
Source:
Zbl
Classification : 35B45, 35A08, 35K10 
@article{PMATES_2004__48_2_41508,
     author = {Steve Hofmann and Seick Kim},
     title = {Gaussian estimates for fundamental solutions to certain parabolic systems.},
     journal = {Publicacions Matem\`atiques},
     pages = {481-496},
     volume = {48},
     number = {2},
     year = {2004},
     zbl = {an:1061.35023},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/PMATES_2004__48_2_41508/}
}
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Steve Hofmann; Seick Kim. Gaussian estimates for fundamental solutions to certain parabolic systems.. Publicacions Matemàtiques, Tome 48 (2004) no. 2, p. 481-496. https://geodesic-test.mathdoc.fr/item/PMATES_2004__48_2_41508/