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arXiv · 1707.09162

Fundamental solutions for second order parabolic systems with drift terms

Hongjie Dong·Seick Kim
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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 $BMO^{-1}_x$, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bound for such fundamental solutions under the same conditions.

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Hongjie Dong, Seick Kim. 2017-07-28. Fundamental solutions for second order parabolic systems with drift terms. https://doi.org/10.1090/proc/14004

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