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A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger

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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.