We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.
© 2001 Society for Inudstrial and Applied Mathematics
Castro, Alfonso and Neuberger, J. W., "A Local Inversion Principle of the Nash-Moser Type" (2001). All HMC Faculty Publications and Research. 479.