论文标题
平面BV同构的面积分段限制的分类
Classification of area-strict limits of planar BV homeomorphisms
论文作者
论文摘要
我们提出了平面$ bv $同态的面积限制的分类。这类映射可以进行空洞和断裂，但可以实现对INV条件的合适概括。正如J. Ball [4]所指出的那样，这些特征是在弹性变形的极限配置中预期的。在[12]中，de Philippis和Pratelli引入了\ emph {no-crossing}条件，该条件表征了$ w^{1，p} $封闭平面同构的闭合。在当前的论文中，我们表明，此概念的合适版本与地图，$ f $，是BV同构的面积限制。这将我们的结果从[10]扩展到[10]，我们证明了BV地图的\ emph {no-crossing bv}条件相当于同构的M-Strict限制（即$ f_k $ convery $ w^*$ to $ w^*$ to $ f $ f $ f $ and $ f $ and $ | d_1f_k | d_1f_k |（ω） | d_1f |（ω）+| d_2f |（ω）$）。此外，我们表明\ emph {no-crossing bv}条件等效于同一条件的看似更强的版本。
We present a classification of area-strict limits of planar $BV$ homeomorphisms. This class of mappings allows for cavitations and fractures but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball [4], these features are expected in limit configurations of elastic deformations. In [12], De Philippis and Pratelli introduced the \emph{no-crossing} condition which characterizes the $W^{1,p}$ closure of planar homeomorphisms. In the current paper we show that a suitable version of this concept is equivalent with a map, $f$, being the area-strict limit of BV homeomorphisms. This extends our results from [10], where we proved that the \emph{no-crossing BV} condition for a BV map was equivalent with the map being the m-strict limit of homeomorphisms (i.e. $f_k$ converges $w^*$ to $f$ and $|D_1f_k|(Ω)+|D_2f_k|(Ω) \to |D_1f|(Ω)+|D_2f|(Ω)$). Further we show that the \emph{no-crossing BV} condition is equivalent with a seemingly stronger version of the same condition.
