Scholarlink

In the Dirichlet boundary value problem, a function \(u = u(x,y)\) is sought, which is a solution of the Laplace equation \(\Delta u = u_{xx} + u_{yy} = 0\) in a domain D and takes on given (boundary) values on the boundary of D. The solutions of the Laplace equation \(\Delta u = 0\) are the harmonic functions. These are precisely the real and imaginary parts of holomorphic functions.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Harmonic Functions and the Dirichlet Boundary Value Problem

  • 章节

  • 发表日期：

    2026年

查看全文
  • Christian Karpfinger

摘要

In the Dirichlet boundary value problem, a function \(u = u(x,y)\) is sought, which is a solution of the Laplace equation \(\Delta u = u_{xx} + u_{yy} = 0\) in a domain D and takes on given (boundary) values on the boundary of D. The solutions of the Laplace equation \(\Delta u = 0\) are the harmonic functions. These are precisely the real and imaginary parts of holomorphic functions.