Asymptotics of Green’s functions in the shadow. (English) Zbl 0626.35018
Three theorems are given including sketches of their proofs. They deal with the resolvent of \((-\Delta -k^ 2)\) in a domain D in \({\mathbb{R}}^ n\), and in \(\pm Im k>0\). In each case with respect to k the first theorem concerns analytic continuation of the resolvent, the second is an estimate for Green’s function, and the third gives an inequality for the solution of a scattering problem.
Reviewer: K.Habetha
MSC:
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35P25 | Scattering theory for PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
35C15 | Integral representations of solutions to PDEs |
35B35 | Stability in context of PDEs |