On the successive approximation of classical solutions for multi-surface free-boundary problems with general non-linear joining conditions

We prove the global convergence of an analytical trial free-boundary algori thm, called the operator method, in the context of a very large class of mu ltiple-free-boundary problems in R-N, N greater than or equal to 2. We stud y the general case of a finite number of annular ow-layers, having a nested family of closed, (N - 1)-dimensional hypersurfaces as interfaces. Each in terface is characterized by a general non-linear joining condition relating the normal derivatives of the stream functions in the two adjoining layers .