关于逆的分布调节与导数
On distributional adjugate and derivative of the inverse
摘要：
设$Ω\subset\er^3$是一个域，$f\colonΩ\to\er^3$是一个双$BV$同胚.最近在\cite{HKL}中，证明了$Df$（因此也是$Df^{-1}$）的分布佐剂是矩阵值测度。本文证明了$\Adj Df$的分量与$Df^{-1}(f(U))$的分量作为测度是相等的，并且证明了分布伴随$\Adj Df$的绝对连续部分等于逐点伴随$\adj Df(x)$ a.e.我们还证明了等价的几种方法的定义的分配的adjugate。
英文摘要：
Let $Ω\subset\er^3$ be a domain and let $f\colonΩ\to\er^3$ be a bi-$BV$ homeomorphism. Very recently in \cite{HKL} it was shown that the distributional adjugate of $Df$ (and thus also of $Df^{-1}$) is a matrix-valued measure. In the present paper we show that the components of $\Adj Df$ are equal to components of $Df^{-1}(f(U))$ as measures and that the absolutely continuous part of the distributional adjugate $\Adj Df$ equals to the pointwise adjugate $\adj Df(x)$ a.e. We also show the equivalence of several approaches to the definition of the distributional adjugate.
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