Article

Archiv der Mathematik

, Volume 93, Issue 2, pp 181-190

First online:

Explicit approximation of the symmetric rearrangement by polarizations

  • Jean Van SchaftingenAffiliated withDépartement de Mathématique, Université catholique de Louvain Email author 

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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 rearrangement Schwarz symmetrization Polarization Two-point rearrangement Pólya–Szegő inequality Approximation of symmetrization Steiner symmetrization Foliated Schwarz symmetrization Spherical cap rearrangement Discrete rearrangement

Mathematics Subject Classification (2000)

Primary 26D15 Secondary 35A25