On Frechet differentiability of some nonlinear operators occurring in inverse problems: an implicit function theorem approach

The validity of Newton-Kantorovich methods for the computational solution of inverse problems is directly linked to the Frechet differentiability of the appropriate nonlinear operator. The authors illustrate how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. Two widely studied boundary and exterior measurement inverse problems are considered and new regularity results are produced.