Fundamental solutions for second order parabolic systems with drift terms

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 $BM{O}_x^{-1}$, 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.

11 pages, minor correction

References in corpus (1)

• On the Green's matrices of strongly parabolic systems of second order

Cited by in corpus (1)

• $L^p$ theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part