Arkiv för Matematik

  • Ark. Mat.
  • Volume 43, Number 2 (2005), 323-345.

Total curvature and rearrangements

Björn E. J. Dahlberg

Full-text: Open access

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.

Note

This posthumous paper was prepared for publication by Vilhelm Adolfsson and Peter Kumlin.

Note

The author was supported by a grant from the Swedish Natural Science Research Council.

Article information

Source
Ark. Mat., Volume 43, Number 2 (2005), 323-345.

Dates
Received: 9 March 2004
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898903

Digital Object Identifier
doi:10.1007/BF02384783

Mathematical Reviews number (MathSciNet)
MR2173955

Zentralblatt MATH identifier
1088.26003

Rights
2005 © Institut Mittag-Leffler

Citation

Dahlberg, Björn E. J. Total curvature and rearrangements. Ark. Mat. 43 (2005), no. 2, 323--345. doi:10.1007/BF02384783. https://projecteuclid.org/euclid.afm/1485898903


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References

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