Nonlinear generalizations of the Banach-Stone theorem
Nonlinear integral operators on C(S,E)
Nonlinear Maps between Besov and Sobolev spaces
Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].
Nonlinear transformations on spaces of continuous functions