Green's Function - Further Examples

Further Examples

  • Let n = 1 and let the subset be all of R. Let L be d/dx. Then, the Heaviside step function H(x − x0) is a Green's function of L at x0.
  • Let n = 2 and let the subset be the quarter-plane { (x, y) : x, y ≥ 0 } and L be the Laplacian. Also, assume a Dirichlet boundary condition is imposed at x = 0 and a Neumann boundary condition is imposed at y = 0. Then the Green's function is
\begin{align} & {} \quad G(x, y, x_0, y_0) \\ & = \dfrac{1}{2\pi}\left \\ & {} \quad {}+\dfrac{1}{2\pi}\left \end{align}

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