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Total curvature and rearrangements.

Björn E. J. Dahlberg (Institutionen för matematiska vetenskaper)
Arkiv för matematik (0004-2080). Vol. 43 (2005), 2, p. 323-345.
[Artikel, refereegranskad vetenskaplig]

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 inL 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.

Nyckelord: total curvature, rearrangement

Björn Dahlberg deceased on the 30th of January 1998. It was Björn's intention to submit this paper for publication, but this was prevented by his untimely death. His results of this paper were presented in October 1997 at the MSRI, Berkeley, during the program Harmonic Analysis and Applications to PDEs and Potential Theory. Independently similar results were obtained by A. Cianchi [1]. The final version of this paper was prepared by Vilhelm Adolfsson and Peter Kumlin, Dept. of Mathematics, Chalmers University of Technology and Göteborg University. email: vilhelm@chalmers.se

Denna post skapades 2010-02-16. Senast ändrad 2010-02-24.
CPL Pubid: 112512


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