Boundary value problems of mathematical physics
Boundary value problems of mathematical physics
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DOI：
10.1007/978-1-4757-4317-3
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
O. A. Ladyzhenskai︠a︡
中科院分区：
文献类型：
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作者：
O. A. Ladyzhenskai︠a︡
在本版本中，我在每章末尾都加入了“补充和问题”。这样做的目的是说明书中所包含的方法的可能性，以及我多年来试图为我的学生做的事情唤醒他们的创造力，为独立工作提供主题。我自己最初的研究来源于著名的两卷本《数学物理方法》，作者D。Hilbert和R.柯朗，以及一系列关于偏微分方程及其在理论力学和物理问题中的应用的原创文章和调查。K. O.弗里德里希，这是在符合我自己的看法的主题，有一个特别强烈的影响我。我是由愿望证明，尽可能简单，这就像系统的n个线性代数方程在n个未知数，基本边值问题可解性（和初边值）问题是”充分大”空间中唯一性定理的一个结果函数空间这一愿望成功地实现了由于引进了各类一般的解决方案，并阐述了相应的唯一性定理的证明方法。这是完成的基础上比较简单的积分不等式的任意功能和先验估计的解决方案的问题，而不征任何特殊表示这些解决方案。
In the present edition I have included" Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a" sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.