正则性方法的内涵与理解  

The Connotation and Understanding of Regularity Method

作　　者：曹志杰 CAO Zhijie(College of Science,China Three Gorges University,Yichang,Hubei Province,443002 China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《科技资讯》2022年第23期232-236,共5页Science & Technology Information

摘　　要：与微分方程解的适定性或不适定性比较,解的正则性的具体涵义不是很确定。除了微分方程的解,数学学科中很多对象都有正则性研究,并且,不同的数学对象有不同的正则性,不同的方法有不同的正则性的研究方法。该文从黎曼积分的定义、一般函数的磨光及微分方程的广义解的意义这3个方面,详细论述这些解的正则性及为什么要研究它们的正则性。最后给出了作者对正则性涵义的一般理解。Compared with the well-posedness or ill-posedness of the solutions of differential equations,the specific meaning of the regularity of the solutions is not very certain.In addition to the solutions of differential equations,many objects in mathematics discipline have regularity research,and different mathematical objects have different regularity,and different methods have different regularity research methods.From three aspects:the definition of Riemann Integral,the mollification of general functions and the meaning of generalized solutions of differential equations,this paper discusses in detail the regularity of these solutions and why we should study their regularity.Finally,the author's general understanding of the meaning of regularity is given.

关 键 词：正则性 黎曼积分 卷积 广义导数 

分 类 号：O152.7[理学—数学]