李斯特·L·海尔姆斯的《potential理论》

English | PDF (True) | 2009 | 442 Pages | ISBN : 1848823185 | 3.5 MB

The ?rst six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. Atthetimeof the writing of that book, I had access to excellent articles,books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A n- comer to the subject will ?nd the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the Am- ican Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “. . . When I read a journal article, I often ?nd mistakes. Whether I can ?x them is irrelevant. The literature is unreliable. ” From time to time, someone must try to ?nd a path through the maze. In planning this book, it became apparent that a de?ciency in the 1969 book would have to be corrected to include a discussion of the Neumann problem, not only in preparation for a discussion of the oblique derivative boundary value problem but also to improve the basic part of the subject matter for the end users, engineers, physicists, etc.

这本书的前六章是作者1969年著作《势理论简介》中同一章节的修订版本。在撰写那本书的时候，我有机会接触到许多M. Brelot的文章、书籍和讲义。这些作品的清晰性使将它们整合成一个整体的任务变得更加容易。不幸的是，并没有相关集子能够反映近年来势理论的发展。对于该领域的初学者来说，期刊文献就像一个迷宫，既有优秀的论文也有不该发表的论文。美国数学协会2008年8月号《 Notices》专栏评论中，莱曼学院（CUNY）和研究生中心M. Nathanson说：“当我阅读一篇期刊文章时，经常发现错误。是否能修正它们无关紧要，因为文献不可靠。” 在计划撰写这本书的过程中逐渐显现出1969年的著作中存在的一个缺陷需要加以弥补以讨论Neumann问题，不仅是为了准备讨论斜导数边值问题，而且为了提高最终用户如工程师、物理学家等该领域的基础部分。

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