论文标题
与测量数据的发散方程的加权lebesgue空间的可溶性
Solvability In Weighted Lebesgue Spaces of the Divergence Equation with Measure Data
论文作者
论文摘要
在以下论文中，一项研究，考虑到有界的，连接的开放式$ω$ $ \ subseteq $ r n，$κ$> 0，一个正ra量$μ$ 0 in $ω$和a（签名的）radon量$μ$ on $ω$ on $ω$满足$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ | $κ$$μ$ 0，求解方程式div u = $μ$的可能性是vector Field u满足| U | $κ$ w在$ω$上（其中W是一种可集成的重量，仅与$ω$和$μ$ 0相关的几何形状），以及轻度的边界条件。这扩展了方程div u = f在[4]中获得的结果，在两个方面改进了它们：一个方面与测量数据的发散方程一起起作用，并且还构建了一个重量W，以较柔和的方式依赖于$ω$的几何形状，从而在某些情况下基本上改善了其行为（从而改善了解决方案的先验行为）。本文中使用的方法遵循Bogovskii类型的建设性方法。
In the following paper, one studies, given a bounded, connected open set $Ω$ $\subseteq$ R n , $κ$ > 0, a positive Radon measure $μ$ 0 in $Ω$ and a (signed) Radon measure $μ$ on $Ω$ satisfying $μ$($Ω$) = 0 and |$μ$| $κ$$μ$ 0 , the possibility of solving the equation div u = $μ$ by a vector field u satisfying |u| $κ$w on $Ω$ (where w is an integrable weight only related to the geometry of $Ω$ and to $μ$ 0), together with a mild boundary condition. This extends results obtained in [4] for the equation div u = f , improving them on two aspects: one works here with the divergence equation with measure data, and also construct a weight w that relies in a softer way on the geometry of $Ω$, improving its behavior (and hence the a priori behavior of the solution we construct) substantially in some instances. The method used in this paper follows a constructive approach of Bogovskii type.
