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Nonlinear Maps between Besov and Sobolev spaces

Philip BrennerPeter Kumlin — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

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].

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