论文标题
多极电位和加权强壮的不平等现象
Multipolar potentials and weighted Hardy inequalities
论文作者
论文摘要
\ begin {摘要} 在本文中，我们指出，在加权Sobolev空间中的任何功能的任何功能$φ$的加权型不平等和重量函数$μ$ $ $ $ never type \ begin \ begin {equation*} c_ {n，μ} \ int _ {\ int _ {\ r^n} φ|^2μ（x）dx +c_μ\ int _ {\ r^n}wφ^2μ（x）dx，\ end \ end {equation*}，其中$ v $是多极性电位，$ w $是从上面依靠$μ$的界限。获得结果的方法是基于引入合适的矢量值函数以及我们在本文中陈述的积分身份。我们证明，通过构建合适的函数序列，估算中常数$ c_ {n，μ} $是最佳的。 \ end {摘要}
\begin{abstract} In this paper we state the following weighted Hardy type inequality for any functions $φ$ in a weighted Sobolev space and for weight functions $μ$ of a quite general type \begin{equation*} c_{N,μ} \int_{\R^N}V\,φ^2μ(x)dx\le \int_{\R^N}|\nabla φ|^2μ(x)dx +C_μ\int_{\R^N}W φ^2μ(x)dx, \end{equation*} where $V$ is a multipolar potential and $W$ is a bounded function from above depending on $μ$. The method to get the result is based on the introduction of a suitable vector value function and on an integral identity that we state in the paper. We prove that the constant $c_{N,μ}$ in the estimate is optimal by building a suitable sequence of functions. \end{abstract}
