若干函数连续性与间断性的理论与应用拓展  

Some Generalizations of Continuity and Discontinuity of a Function and Its Applications

作　　者：詹华税 许文彬[2] ZHAN Huashui;XU Wenbin(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China;School of Sciences,Jimei University,Xiamen 361021,China)

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024 [2]集美大学理学院,福建厦门361021

出　　处：《厦门理工学院学报》2021年第1期79-84,共6页Journal of Xiamen University of Technology

基　　金：福建省自然科学基金项目(2019J01858)。

摘　　要：为进一步充实经典数学分析的理论研究,对变上限积分的连续性与可导性问题展开分析。并利用函数连续性的最值原理,讨论具有连续偏导数的三元函数梯度存在性问题;并基于BV函数的基本性质,讨论一类金融数学方程BV解的间断点分布的几何性质。结果表明,变上限积分函数是几乎处处可导的函数,比一般的连续函数具有更好的可利用的分析性质;一般可微函数未必存在梯度。文中同时证明了上述金融数学方程BV解的间断点集合是一曲线,而不可能是一曲面。In order to enrich the classical mathematical analysis theory,this paper probes the continuity and derivability of a variable upper bound integral function,uses the maximum principle of the continuity of the function to discuss the existence of the gradient of a three-dimensional function which is with continuous partial derivatives,and discusses the distribution of the discontinuous points of the BV solutions to a class of equation arising from mathematical finance by some properties of a BV function.The results show that the variable upper bound integral function is derivative almost everywhere,possessing therefore a better analytic property than that of a continuous function,and that differential function is not necessarily defined as gradient.It is also proved that the discontinuous points of the BV solutions to the studied finance mathematics equation is a curve rather than a surface.

关 键 词：函数连续性 间断点 变上限积分 金融数学 BV解 

分 类 号：O172.2[理学—数学] O175.29[理学—基础数学]