STEINER SYMMETRIZATION IS CONTINUOUS IN W-1,W-P

Authors
BURCHARD A
Citation
A. Burchard, STEINER SYMMETRIZATION IS CONTINUOUS IN W-1,W-P, Geometric and functional analysis, 7(5), 1997, pp. 823-860
Citations number
48
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Geometric and functional analysis → ACNP
ISSN journal
1016443X
Volume
7
Issue
5
Year of publication
1997
Pages
823 - 860
Database
ISI
SICI code
1016-443X(1997)7:5<823:SSICIW>2.0.ZU;2-Q
Abstract
We study the continuity, smoothing, and convergence properties of Stei ner symmetrization in higher space dimensions. Our main result is that Steiner symmetrization is continuous in W-1,W-p (1 less than or equal to p < infinity) in all dimensions. This implies that spherical symme trization cannot be approximated in W-1,W-p by sequences of Steiner sy mmetrizations. We also give a quantitative version of the standard ene rgy inequalities for spherical symmetrization.