Green Function of the Laplacian for the Neumann Problem in R n
E. Constantin, Nicolae H. Pavel · LIBERTAS MATHEMATICA (vol.I-XXXI) · 2010
By analogy with the Green function for the Dirichlet problem for a domain , one considers the Green type function for the Neumann problem for . We obtain the Green type function for the positive half-space of R n and use it to solve the Neumann problem. The cases where is the positive half space of R 2 and of R 3 are analyzed in details under new hypotheses.