关于BV同胚
On BV homeomorphisms
摘要：
我们得到了平面上有界变差同胚$f$的图的可求正性以及$f$与其逆的梯度之间的关系。进一步，我们给出了一个平面上有界变差同胚$f$的例子，它满足$(N)$和$(N^{-1})$性质以及它自身和它的逆的Jacobian的严格正性，但$f$和$f^{-1}$都不是Sobolev.
英文摘要：
We obtain the rectifiability of the graph of a bounded variation homeomorphism $f$ in the plane and relations between gradients of $f$ and its inverse. Further, we show an example of a bounded variation homeomorphism $f$ in the plane which satisfies the $(N)$ and $(N^{-1})$ properties and strict positivity of Jacobian of both itself and its inverse, but neither $f$ nor $f^{-1}$ is Sobolev.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
