论文标题
关于Monge-Ampe`RE类型方程的第二个导数估计的注释
A note on second derivative estimates for Monge-Ampe`re type equations
论文作者
论文摘要
在本说明中，我们重新访问了作者F. Jiang和J. Liu的先前的Pogorelov型内部和全局第二个衍生估计，以供Monge-Amp`型偏微分方程解决方案。考虑到Guillen，Kitagawa和Rankin的最新严格凸定期结果，以及在最佳运输案例中的早期工作之后，我们在更一般的Jacobian方程式中删除了单调性假设，因此在生成的Jacobian方程式中，以及随后在经典的求解性和第二个边界价值问题的全球规则性方面的应用中。
In this note we revisit previous Pogorelov type interior and global second derivative estimates of the author, F. Jiang and J. Liu for solutions of Monge-Amp`ere type partial differential equations. Taking account of recent strict convexity regularity results of Guillen, Kitagawa and Rankin, and following our earlier work in the optimal transportation case, we remove the monotonicity assumptions in the more general case of generated Jacobian equations and consequently in the subsequent application to classical solvability and global regularity for second boundary value problems.
