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Differentiability and continuity properties of solutions of certain partial differential equations of applied mathematics.

机译：应用数学中某些偏微分方程解的可微性和连续性。

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摘要

Solutions, in the form H/r, of the homogeneous linear partial differential equation of the second order with constant coefficients are used as generalized potential functions. With the aid of generalized Green's theorems and the methods developed by Erhardt Schmidt, it is possible to obtain the breaks in the derivatives of the generalized potentials due to a volume, simple surface and double surface distribution.; When the functions involved satisfy certain differetiability and continuity conditions, it is shown that the breaks in the (n + 1)st order derivatives of these generalized potentials are given by recursion. For example, the breaks in the (n + 1)st order derivatives of the generalized volume potential are obtained from the breaks in the nth order derivatives of potential due to a volume and simple surface distribution. Similar relations are shown to exist for the breaks in the (n + 1)st order derivatives of the generalized potential due to simple surface and double surface distribution.; In chapter IV the theory has been applied to two problems and the breaks in the potentials and their first and second order derivatives have been found for the case of the x3 axis parallel to the normal at the point.
机译：具有常数系数的二阶齐次线性偏微分方程的形式为H / r的解被用作广义势函数。借助于广义格林定理和艾哈特·施密特（Erhardt Schmidt）开发的方法，由于体积，简单的表面和双重表面分布，有可能获得广义势导数的突破。当所涉及的函数满足一定的可微性和连续性条件时，表明这些广义势的（n + 1）阶导数的中断是通过递归给出的。例如，由于体积和简单的表面分布，可以从电势的n阶导数的断裂中获得广义体积电势的（n +1）阶导数的断裂。由于简单的表面和双重表面分布，对于广义电势的（n +1）阶导数的断裂，显示存在相似的关系。在第四章中，该理论已应用于两个问题，并且在x3轴与该点的法线平行的情况下，发现了电位的中断及其一阶和二阶导数。

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  • 作者

    Davis, Arthur W.;

  • 作者单位

    Iowa State University.;

  • 授予单位 Iowa State University.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 1939
  • 页码 43 p.
  • 总页数 43
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

  • 入库时间 2022-08-17 11:52:13

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