Second-Order Equations With Nonnegative Characteristic Form
Second-Order Equations With Nonnegative Characteristic Form
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DOI：
10.1007/978-1-4684-8965-1
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发表时间：
1973-11
期刊：
影响因子：
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通讯作者：
O. Oleinik;E. Radkevich;P. Fife
中科院分区：
文献类型：
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作者：
O. Oleinik;E. Radkevich;P. Fife
具有非负特征形式的二阶方程是偏微分方程理论的一个新分支，产生于近20年，并在近年来得到了特别深入的发展。 (1) 形式的方程被称为集合 G, kj 上的具有非负特征形式的二阶方程，如果在属于 G 的每个点 x 对于任何向量都有一个 (xHk~ j~ 0 对于任何向量 ~=(~ l'...'~ m)' 在方程 (1) 中，假设重复索引从 1 到 m 求和，并且 x=(x l'•••, x)。这样的方程有时也称为退化 m 椭圆方程或这类方程包括椭圆和抛物型方程、一阶方程、超抛物型方程、布朗运动方程等。具有非负特征形式的二阶方程的一般理论的基础已经建立，本书的目的是提出这种基础形式的方程（1），与经过充分研究的椭圆或抛物型方程不相符。很久以前就对此进行了研究，特别是在大约 60 年前发表的 Picone [105] 论文中。
Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~ j~ 0 for any vector~=(~ l'...'~ m)'In equation (1) it is assumed that repeated indices are summed from 1 to m, and x=(x l'•••, x). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone [105], published some 60 years ago.