Interpolation spaces in the resolution of ill-posed problems

A number of applied problems connected with the interpretation of geophysical data leads to the resolution of ill-posed problems of the form A x = yδ, where A is an integral operator and yδ - some measurements. In the resolution of these problems by the Tikhonov's variational method, the choice of the stabilizing functional is crucial and needs some a-priori informations about the exact solution. Here the norm of the interpolation spaces Xθ,q, which depends on two parameters 0 < θ < 1, 1 ≤ q < ∞ is proposed as a stabilizing functional. The a-priori information about the exact solution is characterized by its membership in one of the interpolation spaces. (author). 9 refs