Green’s Function and Its Properties

In this section, we would like to discuss Dirichlet boundary-value problem. The method is to use Green’s identity and Green’s second formula to transform the problem to another specialized Dirichlet boundary-value problem. In the process, we naturally derive Green’s function.

Generally speaking, There are two class of Dirichlet boundary-value problem for elliptic partial equations, i.e., the Dirichlet problem of harmonic equation
\begin{equation}
\begin{cases}
\Delta u=0, &\text{in }\Omega\\
u=\phi,&\text{on }\pt\Omega,
\end{cases}
\end{equation}
Continue Reading

Suggestions for Visitors and Writers

This post is quite important, which includes suggestions on what you can do to improve your experience of browsing and some problems when you try to post some stuff on this site.

For Visitors:

  1. First of first, is that you should use Chorme 16, FireFox 7.8, IE 9.0 or upper browser.
  2. In case your browser is satisfied, but the math formula is not rendered, please first make sure that you can visit the MathJax, since the math render rely on it, and then empty your cache and refresh the page
  3. Continue Reading