A priori limitations for solutions of Monge-Ampère equations. II
A priori limitations for solutions of Monge-Ampère equations. II
复制标题
Monge-Ampère 方程解的先验限制。
DOI：
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发表时间：
1937
期刊：
影响因子：
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通讯作者：
H. Lewy
中科院分区：
文献类型：
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作者：
H. Lewy
本文研究椭圆型和解析型Monge-Ampere方程解的收敛性。定理1给出了本文的主要结果。第372页的例子指出了某些类型的奇点的可能性，而这些奇点对于线性椭圆方程是不可能出现的。定理2和定理3给出了极限函数解析的充分条件。这些条件允许应用到某些问题的微分几何在大。我们的方法包括在引入一个正则化的接触变换，它将凸函数的功能与有界的二阶导数，从而使定理1的主要结果，本文的第一部分减少。1.规范接触变换。考虑一个（x，y，z）-空间到一个（x，-q，）-空间的切触变换T，它由以下关系生成：
In this paper we are concerned with the convergence of solutions of elliptic and analytic Monge-Ampere equations. Theorem 1 gives the principal result of this paper. The example on p. 372 indicates the possibility of certain types of singularities which for linear elliptic equations cannot occur. Theorems 2 and 3 give sufficient conditions for the analyticity of the limit function. These conditions allow applications to certain problems of the differential geometry in the large. Our method consists in introducing a regularizing contact transformation which transforms convex functions into functions with bounded second derivatives and thus makes possible the reduction of Theorem 1 to the principal result of the first part of this paper. 1. Regularizing contact transformation. Consider the contact transformation T of an (x, y, z)-space into a (%, -q, )-space generated by the relation