Archiv der Mathematik

, Volume 93, Issue 2, pp 181–190

Explicit approximation of the symmetric rearrangement by polarizations

Article

DOI: 10.1007/s00013-009-0018-3

Cite this article as:
Van Schaftingen, J. Arch. Math. (2009) 93: 181. doi:10.1007/s00013-009-0018-3

Abstract

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.

Keywords

Symmetric rearrangementSchwarz symmetrizationPolarizationTwo-point rearrangementPólya–Szegő inequalityApproximation of symmetrizationSteiner symmetrizationFoliated Schwarz symmetrizationSpherical cap rearrangementDiscrete rearrangement

Mathematics Subject Classification (2000)

Primary 26D15Secondary 35A25

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Département de MathématiqueUniversité catholique de LouvainLouvain-la-NeuveBelgium