狄利克雷原理历史探源  

Exploration of the Origin of the Dirichlet Principle

作　　者：耿锦铭 李威[1] GENG Jinming;LI Wei(Institute for Advanced Studies in History of Science,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学科学史高等研究院,陕西西安710127

出　　处：《广西民族大学学报（自然科学版）》2024年第1期59-65,73,共8页Journal of Guangxi Minzu University ：Natural Science Edition

摘　　要：狄利克雷原理起源于物理问题,是研究偏微分方程论和变分法的重要工具,数学和物理中的许多重要定理都是在此原理的基础上建立的。文章在“为什么数学”的研究范式下,采用路线图的研究方法,在原始文献和研究文献的基础上,整理和分析黎曼提出狄利克雷原理的物理动因和函数论思想动因,探究了黎曼两篇论文中关于狄利克雷原理的提出及证明过程,探寻狄利克雷原理来源中的思想传承脉络,推出黎曼提出狄利克雷原理是受到了多位数学家的启发和影响,有助于我们更为清晰地理解黎曼函数理论的基础核心问题。Dirichlet principle is an important tool for the study of partial differential equations and Calculus of Variations and many important theorems in mathematics and physics are based on this principle.In this paper,we adopt a route-map research method under the paradigm of"Why mathematics",based on the original literature and research literature,organize and analyze the physical motivation and function theory idea motivation of Riemann's Dirichlet principle,explore the process of proposing and proving it in two papers of Riemann,explore the idea of the origin of Dirichlet principle.It is also explored that Riemann's Dirichlet principle was inspired and influenced by several mathematicians,which helps us to understand the core problems of Riemann's function theory more clearly.

关 键 词：黎曼 狄利克雷原理 狄利克雷积分 

分 类 号：N09[自然科学总论—科学技术哲学]