TY - JOUR
T1 - Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
AU - Kim, Seick
PY - 2008/11
Y1 - 2008/11
N2 - Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on ℝn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.
AB - Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on ℝn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.
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U2 - 10.1090/S0002-9947-08-04485-1
DO - 10.1090/S0002-9947-08-04485-1
M3 - Article
AN - SCOPUS:54049108773
SN - 0002-9947
VL - 360
SP - 6031
EP - 6043
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 11
ER -