Nash-Moser theorem
From Wikipedia, the free encyclopedia
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.
[edit] Further reading
- Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser" (PDF-12MB). Bulletin of the American Mathematical Society 7 (1): 65–222. doi:.. (A detailed exposition of the Nash-Moser theorem and its mathematical background.)
