Some estimates of Green’s functions in the shadow. (English) Zbl 0656.35022

Popov, Georgi

Osaka J. Math. 24, 1-12 (1987).

The purpose of this work is to investigate the asymptotic behaviour of Green’s functions in the so-called shadow for Laplace operator in an exterior domain. As a consequence a field scattered by a non-trapping obstacle will be examined at high frequencies.

MSC:

35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P25	Scattering theory for PDEs
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

asymptotic behaviour; Green’s functions; shadow; Laplace operator; exterior domain; non-trapping obstacle