I have recently been learning the theory of Banach manifolds through Serge Lang's book on Differential Manifolds. So far the objects seem rather interesting but my intuition always comes from the finite dimensional case, which admittedly is very helpful but I certainly want to add onto this.

I am wondering if there is a reference where one has examples of Banach manifolds where the tangent spaces are function spaces (ie Sobolev spaces). Obviously, I would like to avoid the trivial example of the function space being the manifold.

In some sense I would like an example that embraces the infinite dimensional tangent space as well as giving me some understanding as to what the topological space/smooth structure should be in the setting.

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