论文标题
Zvonkin的变换和解决方案的规律性双发差异形成椭圆方程
Zvonkin's transform and the regularity of solutions to double divergence form elliptic equations
论文作者
论文摘要
我们在〜$ \ mathbb {r}^d $上研究解决方案的定性属性。结果表明，如果扩散矩阵$ a $是非排效的，并且满足DINI平均振荡条件，并且漂移系数$ b $在本地集成到功率$ p> d $，则harnack不等式对于非负解决方案而言。我们为解决方案的$ l^p $ norms建立了新的估计，并获得了Hasminskii定理的概括性，该定理对存在于固定的kolmogorov方程的概率解决方案对矩阵$ a $满足Dini的状况或属于VMO级别的情况。这些结果基于Zvonkin的漂移系数变换的新分析版本。
We study qualitative properties of solutions to double divergence form elliptic equations (or stationary Kolmogorov equations) on~$\mathbb{R}^d$. It is shown that the Harnack inequality holds for nonnegative solutions if the diffusion matrix $A$ is nondegenerate and satisfies the Dini mean oscillation condition and the drift coefficient $b$ is locally integrable to a power $p>d$. We establish new estimates for the $L^p$-norms of solutions and obtain a generalization of the known theorem of Hasminskii on the existence of a probability solution to the stationary Kolmogorov equation to the case where the matrix $A$ satisfies Dini's condition or belongs to the class VMO. These results are based on a new analytic version of Zvonkin's transform of the drift coefficient.
