论文标题
椭圆方程从弱的莫雷空间偏僻
Elliptic equations with a singular drift from a weak Morrey space
论文作者
论文摘要
在本文中，我们证明了椭圆形方程的弱解决方案的存在和唯一性，带有漂移$ b $满足$ \ operatatorName {div} b \ le 0 $ in $ω$中的椭圆形方程。我们假设$ b $属于一些弱的莫雷类，其中包括3D情况下，尤其是在轴上具有奇异性$ x_3 $，渐近$ b（x）\ sim c/r $，其中$ r = \ sqrt {x_1^2^2+x_2^2} $。
In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift $b$ satisfying $\operatorname{div} b\le 0$ in $Ω$. We assume $b$ belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where $r=\sqrt{x_1^2+x_2^2}$.
