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Universal approximation of symmetrizations by polarizations


Author: Jean van Schaftingen
Journal: Proc. Amer. Math. Soc. 134 (2006), 177-186
MSC (2000): Primary 26D10; Secondary 28D05, 46E30
DOI: https://doi.org/10.1090/S0002-9939-05-08325-5
Published electronically: August 11, 2005
MathSciNet review: 2170557
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Abstract | References | Similar Articles | Additional Information

Abstract: Any symmetrization (Schwarz, Steiner, cap or increasing rearrangement) can be approximated by a universal sequence of polarizations which converges in $\mathrm{L}^p$ norm for any admissible function in $\mathrm{L}^p$ for $1 \le p < +\infty$ and uniformly for admissible continuous functions. A new Pólya-Szegö inequality is proved for the increasing rearrangement.


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Additional Information

Jean van Schaftingen
Affiliation: Département de Mathématiques, Université Catholique de Louvain, Chemin du cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Email: vanschaftingen@math.ucl.ac.be

DOI: https://doi.org/10.1090/S0002-9939-05-08325-5
Received by editor(s): May 13, 2003
Received by editor(s) in revised form: July 15, 2004
Published electronically: August 11, 2005
Additional Notes: The author is a research fellow of the Fonds National de la Recherche Scientifique (Belgium).
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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