Regularity of monotone transport maps between unbounded domains
Regularity of monotone transport maps between unbounded domains
复制标题
无界域之间单调传输映射的规律性
DOI：
10.3934/dcds.2019297
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
A. Figalli
中科院分区：
文献类型：
--
作者：
D. Cordero;A. Figalli
单调迁移映射的正则性在偏微分方程和几何学的一些应用中起着重要的作用。不幸的是，关于这个问题的经典陈述仅限于紧支撑测度的情况。本文证明了，在几种有趣的情形下，即使测度有无界支撑，也可以保证单调映射的正则性。
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In this note we show that, in several situations of interest, one can to ensure the regularity of monotone maps even if the measures may have unbounded supports.