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

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
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