论文标题
有限失真曲线：连续性，可怜性和Lusin（n）属性
Finite distortion curves: Continuity, Differentiability and Lusin's (N) property
论文作者
论文摘要
我们定义有限失真$ω$ - 曲线，我们表明，对于某些表格$ω$，当失真函数足够指数式地集成时，地图是连续的，几乎在任何地方都可以区分，并且具有Lusin（n）的属性。这是通过有关有限失真$ω$ curves的一些较高可集成性结果来实现的。还表明，对于连续性和Lusin（n）属性，这一结果都是鲜明的。我们还表明，如果我们假设有限失真$ω$ curve的坐标弱单调性，我们将获得连续性。
We define finite distortion $ω$-curves and we show that for some forms $ω$ and when the distortion function is sufficiently exponentially integrable the map is continuous, differentiable almost everywhere and has Lusin's (N) property. This is achieved through some higher integrability results about finite distortion $ω$-curves. It is also shown that this result is sharp both for continuity and for Lusin's (N) property. We also show that if we assume weak monotonicity for the coordinates of a finite distortion $ω$-curve we obtain continuity.
