Continuous dependence of the scattering amplitude on the surface of an obstacle

✍ Scribed by A. G. Ramm

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 280 KB
• Volume: 18
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670180203

✦ Synopsis

Abstract

Let D~j~,j = 1,2, be two bounded domains (obstacles) in ℝ^n^, n ≥ 2, with the boundaries Γ~j~. Let A~j~ be the scattering amplitude corresponding to D~j~. The Dirichlet boundary condition is assumed on Γ~j~. A formula is derived for A:= A~1~ − A~2~. This formula is used for a derivation of the estimate of ∣A~1~ − A~2~∣ in terms of the distance d(Γ~1~, Γ~2~) between Γ~1~ and Γ~2~. If d(Gamma;~1~, Gamma;~2~) ⩽ ϵ, then ∣A∣ ⩽ __c__ϵ, where c is a positive constant which depends on Γ~1~ and Γ~2~ provided that one of the boundaries is of C^1,λ^ class, 0 < λ < 1, and the other one is a polyhedron which approximates the first one. The results are useful, in particular, for boundary elements method of solving scattering problems.