Abstract
We study to what extent rearrangements preserve the integrability properties of higher order derivatives. It is well known that the second order derivatives of the rearrangement of a smooth function are not necessarily in L1. We obtain a substitute for this fact. This is done by showing that the total curvature for the graph of the rearrangement of a function is bounded by the total curvature for the graph of the function itself.
Funding Statement
The author was supported by a grant from the Swedish Natural Science Research Council.
Note
This posthumous paper was prepared for publication by Vilhelm Adolfsson and Peter Kumlin.
Citation
Björn E. J. Dahlberg. "Total curvature and rearrangements." Ark. Mat. 43 (2) 323 - 345, October 2005. https://doi.org/10.1007/BF02384783
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