论文标题
具有粗糙系数的退化kolmogorov方程的最佳规律性
Optimal regularity for degenerate Kolmogorov equations with rough coefficients
论文作者
论文摘要
我们考虑一类退化方程，满足抛物线寄生虫的条件，其系数在时间上可以测量，并且在空间变量中连续hölder连续。通过利用强大解决方案的广义概念，我们确定了基本解决方案的存在及其最佳的Hölder规律性以及高斯估计。这些结果是研究与一类Langevin型扩散相关的向后Kolmogorov方程。
We consider a class of degenerate equations satisfying a parabolic Hörmander condition, with coefficients that are measurable in time and Hölder continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal Hölder regularity, as well as Gaussian estimates. These results are key to study the backward Kolmogorov equations associated to a class of Langevin-type diffusions.
