Ag. Ramm, CONTINUOUS DEPENDENCE OF THE SCATTERING-AMPLITUDE ON THE SURFACE OF AN OBSTACLE, Mathematical methods in the applied sciences, 18(2), 1995, pp. 121-126
Let D-j,j = 1, 2, be two bounded domains (obstacles) in R(n), n greate
r than or equal to 2, with the boundaries Gamma(j). Let A(j) be the sc
attering amplitude corresponding to D-j. The Dirichlet boundary condit
ion is assumed on Gamma(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(Gamma(1), Gamma(2)) between Gamma(1) and
Gamma(2). If d(Gamma(1), Gamma(2)) less than or equal to epsilon, then
\A\ less than or equal to c epsilon, where c is a positive constant w
hich depends on Gamma(1) and Gamma(2) provided that one of the boundar
ies is of C-1,C-lambda class, 0 < lambda < 1, and the other one is a p
olyhedron which approximates the first one. The results are useful, in
particular, for boundary elements method of solving scattering proble
ms.