Nonlinear Maps between Besov and Sobolev spaces
Magazine article, 2010
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  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 .