REGULARIZED SOLUTIONS OF A 3-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE-EQUATION

Using a variational method, the authors give regularized solutions to the problem of determining the index of refraction n in the inhomogeneous wave equation (DELTA + k2 n2(x)) u(x) = F(x) x is-an-element-of OMEGA where OMEGA is a domain in R3, and k > 0 is given. It is assumed that a certain integral quantity, of the nature of a scattering amplitude, is known. Then a = n2 is to be determined in a compact subset of L(infinity) (OMEGA), such that the given integral is closest to a 'measured' value h is-an-element-of R.