Fundamental solutions for second-order parabolic systems with drift terms

Dong, Hongjie; Kim, Seick

doi:10.1090/proc/14004

Fundamental solutions for second-order parabolic systems with drift terms
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by Hongjie Dong and Seick Kim PDF

Proc. Amer. Math. Soc. 146 (2018), 3019-3029 Request permission

Abstract:

We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $\mathrm {BMO}^{-1}_x$, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bounds for such fundamental solutions under the same conditions.

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