Nash-Moser theorem

Nash-Moser theorem

The Nash-Moser theorem, attributed to mathematicians John Forbes Nash and Jurgen Moser is a generalization of the inverse function theorem on Banach spaces to a class of 'tame' Frechet spaces. In contrast to the Banach space case, in which the invertibility of the derivative at a point is sufficient for a map to be locally invertible, the Nash-Moser theorem requires the derivative to be invertible in a neighbourhood. The theorem is widely used to prove local uniqueness for non-linear partial differential equations in spaces of smooth functions.

While Nash is credited with originating the theorem as a step in his proof of the Nash embedding theorem, Moser showed that Nash's methods could be successfully applied to solve problems on periodic orbits in celestial mechanics.

Further reading

  • . (A detailed exposition of the Nash-Moser theorem and its mathematical background.)

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