CONTINUOUS DEPENDENCE OF THE SCATTERING-AMPLITUDE ON THE SURFACE OF AN OBSTACLE

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.