On the Dirichlet problem for Monge-Ampère type equations
On the Dirichlet problem for Monge-Ampère type equations
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DOI：
10.1007/s00526-013-0619-3
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发表时间：
2013-03
影响因子：
2.1
通讯作者：
F. Jiang;N. Trudinger;Xiao-Ping Yang
中科院分区：
文献类型：
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作者：
F. Jiang;N. Trudinger;Xiao-Ping Yang
本文证明了一类Monge-Ampére型方程Dirichlet问题的二阶导数估计及其经典可解性.特别地，我们假设在增广Hessian矩阵函数是正规的Trudinger和王在安。Scoula范数的意义。辅助核算比萨海峡Sci.第八，143-174 2009年在他们的研究全球规律性的最佳运输以及存在一个光滑的子解。后一种假设取代了他们的工作中也使用的障碍条件。文中还指出了该方法在最优运输和雅可比方程中的应用。
In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampére type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143–174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated.