An implicit function theorem for non-smooth maps between Fréchet spaces

Ivar Ekeland; Eric Séré

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arXiv · 1502.01561

An implicit function theorem for non-smooth maps between Fréchet spaces

Ivar Ekeland·Eric Séré

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Abstract

We prove an inverse function theorem of Nash-Moser type for maps between Fréchet spaces satisfying tame estimates. In contrast to earlier proofs, we do not use the Newton method, that is, we do not use quadratic convergence to overcome the lack of derivatives. In fact, our theorem holds when the map to be inverted is not C^2

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Ivar Ekeland, Eric Séré. 2015-02-05. An implicit function theorem for non-smooth maps between Fréchet spaces. https://arxiv.org/abs/1502.01561

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