论文标题
关于当地规定的雅各布方程的理论
On the local theory of prescribed Jacobian equations revisited
论文作者
论文摘要
在本文中，我们重新审视了我们先前对与生成函数相关的处方雅各布方程理论的研究，这是最佳运输理论中成本函数的扩展。特别是，正如较早的工作中所预言的那样，我们提供了与基础凸理论中单调性条件A4W的放松有关的细节以及随之而来的经典规律性。利用了北川和吉伦的最新工作，我们还将经典的规律理论扩展到了关键矩阵凸状条件的弱A3W。
In this paper we revisit our previous study of the local theory of prescribed Jacobian equations associated with generating functions, which are extensions of cost functions in the theory of optimal transportation. In particular, as foreshadowed in the earlier work, we provide details pertaining to the relaxation of a monotonicity condition A4w in the underlying convexity theory and the consequent classical regularity. Taking advantage of recent work of Kitagawa and Guillen, we also extend our classical regularity theory to the weak form A3w of the critical matrix convexity conditions.
