In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ℝ+ 3 with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data.
|Título traducido de la contribución||The Helmholtz equation with impedance in a half-space|
|Número de páginas||6|
|Publicación||Comptes Rendus Mathematique|
|Estado||Publicada - 1 nov 2005|
|Publicado de forma externa||Sí|