For almost one year, I am searching for the Green's function for wave equation in R² or R³ with some boundary conditions. As far as I know, when the boundaries permit the method of images, we can get the Green's function. But this requirement is too strong.
What we would like to have is that: the wave is confined in a convex, sufficiently smooth domain. On the boundary, either Dirichlet or Neumann's conditions can be put. To impose these conditions is just to avoid the diffraction problem, which can be too much complicated for us.
During this searching, I encountered books by Prof. Melrose, Prof. Michael E. Taylor and also the formidable three volumns by Prof. Hormander. I still feel hopeless in finding that.
Thanks in advance for any comments!