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Total curvature and rearrangements

Björn E. J. Dahlberg Department of Mathematics, Chalmers University of Technology

TBD mathscidoc:1701.333060

Arkiv for Matematik, 43, (2), 323-345, 2004.3
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$L$^{1}. 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.
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@inproceedings{björn2004total,
  title={Total curvature and rearrangements},
  author={Björn E. J. Dahlberg},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614715469869},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={2},
  pages={323-345},
  year={2004},
}
Björn E. J. Dahlberg. Total curvature and rearrangements. 2004. Vol. 43. In Arkiv for Matematik. pp.323-345. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614715469869.
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