Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
复制标题
DOI：
10.1090/s0002-9947-08-04485-1
复制
发表时间：
2007-04
影响因子：
1.3
通讯作者：
Seick Kim
中科院分区：
文献类型：
--
作者：
Seick Kim
Auscher，McIntosh和Tchamitchian研究了Rn上具有复有界可测系数的发散型二阶椭圆算子的热核.特别是，在n = 2的情况下，他们得到了高斯上限估计的热核，而不施加进一步的假设的系数。研究了具有有界、可测、与时间无关的系数的散度型二阶抛物型方程组的基本解，并将其结果推广到抛物型方程组.
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on R n . 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.