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

* cite journal
last = Hamilton
first = Richard S.
title = The inverse function theorem of Nash and Moser
journal = Bulletin of the American Mathematical Society
volume = 7
issue = 1
year = 1982
pages = 65–222
url = http://www.ams.org/bull/1982-07-01/S0273-0979-1982-15004-2/S0273-0979-1982-15004-2.pdf
format = PDF-12MB
doi = 10.1090/S0273-0979-1982-15004-2
. (A detailed exposition of the Nash-Moser theorem and its mathematical background.)


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