论文标题
抛物线方程基本解决方案的基本解决方案的估计。
Estimates for fundamental solutions of parabolic equations in non-divergence form
论文作者
论文摘要
我们在空间变量中的DINI平均振荡的假设下，以非差异形式构造二阶抛物线方程的基本解。我们还证明，基本解决方案满足了高斯以下估计。在空间变量中系数是DINI连续的情况下，并且在时间变量中可测量时，我们为基本溶液建立高斯界限。我们提出了一种以非差异形式适用于二阶抛物线系统的方法。
We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution satisfies a sub-Gaussian estimate. In the case when the coefficients are Dini continuous in the spatial variables and measurable in the time variable, we establish the Gaussian bounds for the fundamental solutions. We present a method that works equally for second order parabolic systems in non-divergence form.
