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
\Delta u=0, &\text{in }\Omega\\
u=\phi,&\text{on }\pt\Omega,
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