论文标题
平面Sobolev $ w^{2,1} $同构的近似，分别二次同构和差异性
Approximation of planar Sobolev $W^{2,1}$ homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms
论文作者
论文摘要
给定平面中的w^{2,1} $的sobolev同态$ f \，我们找到了一个分段二次同构同构，将其近似于一组$ε$度量。我们表明，此集合中的$ W^{2,1} $ norm中的差异性可以通过差异性近似。
Given a Sobolev homeomorphism $f\in W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $ε$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the $W^{2,1}$ norm on this set.
