SYMMETRIC POSITIVE LINEAR DIFFERENTIAL EQUATIONS
SYMMETRIC POSITIVE LINEAR DIFFERENTIAL EQUATIONS
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DOI：
10.1002/cpa.3160110306
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发表时间：
1958-01-01
影响因子：
3
通讯作者：
FRIEDRICHS, KO
中科院分区：
文献类型：
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作者：
FRIEDRICHS, KO
由于椭圆型和双曲型微分方程的解具有许多不同的性质，并且必须采用完全不同类型的数据来确定这样的解，因此试图统一处理这些方程似乎是不自然的。本文将在一定程度上给出这样一个统一的处理。这些方程的大多数处理自然会使用完全不同的工具，其中一些使用相同的变体：正定二次型，即所谓的“能量积分”。我们将证明这个工具可以适用于包括经典二阶椭圆型方程和双曲型方程在内的大类微分方程。
Since the solutions of elliptic and hyperbolic differential equations have very many differing properties, and since quite different types of data must be imposed to determine such solutions it would seem unnatural to attempt a unified treatment of these equations. Still such a unified treatment-up to a certain point-will be given in this paper. Mile most of the treatments of these equations naturally employ completely different tools, some of them employ variants of the same: positive definite quadratic forms, the so-called “energy integrals”. We shall show that this tool can be adapted to a large class of differential equations which include the classical elliptic and hyperbolic equations of the second order.