A Local Inversion Principle of the Nash--Moser Type
Copyright policy )A Local Inversion Principle of the Nash--Moser Type
Summary: We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of \textit{J. Moser} [Proc. Natl. Acad. Sci. USA 47, 1824-1831 (1961; Zbl 0104.30503)] 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.
- University of North Texas System United States
- University of North Texas United States
continuous steepest descent, Derivatives of functions in infinite-dimensional spaces, Nonlinear boundary value problems for ordinary differential equations, Nonlinear boundary value problems for linear elliptic equations, inverse function theorem, Nash-Moser methods, Implicit function theorems; global Newton methods on manifolds
continuous steepest descent, Derivatives of functions in infinite-dimensional spaces, Nonlinear boundary value problems for ordinary differential equations, Nonlinear boundary value problems for linear elliptic equations, inverse function theorem, Nash-Moser methods, Implicit function theorems; global Newton methods on manifolds
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