论文标题
适应性和规律性的分配依赖性SPDE具有奇异的漂移
Well-posedness and Regularity for Distribution Dependent SPDEs with Singular Drifts
论文作者
论文摘要
在本文中，研究了与DINI连续漂移的可分离希尔伯特空间中的分布相关的随机微分方程。获得了弱解决方案的存在和独特性。此外，对于相关的半群，得出了一些规律性结果以及梯度估计和对数 - 哈纳克不等式。此外，当噪声是添加剂时，还证明了具有权力和偏移不平等的尺寸不平等不平等。所有结果都扩展了独立的情况下的结果。
In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some regularity results as well as gradient estimates and log-Harnack inequality are derived for the associated semigroup. In addition, dimensional free Harnack inequality with power and shift Harnack inequality are also proved when the noise is additive. All of the results extend the ones in the distribution independent situation.
