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Universal approximation of symmetrizations by polarizations
Author(s):
Jean
van
Schaftingen
Journal:
Proc. Amer. Math. Soc.
134
(2006),
177-186.
MSC (2000):
Primary 26D10;
Secondary 28D05, 46E30
Posted:
August 11, 2005
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Additional information
Abstract:
Any symmetrization (Schwarz, Steiner, cap or increasing
rearrangement) can be approximated by a universal
sequence of
polarizations which converges in
norm for any
admissible function in
for
and
uniformly for admissible continuous functions.
A new
Pólya-Szegö inequality is proved
for the increasing
rearrangement.
References:
-
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- 3.
- A. Baernstein, II, A unified approach to symmetrization, Partial Differential Equations of Elliptic Type (A. Alvino et al., eds.), Sympos. Math., no. 35, Cambridge Univ. Press, 1995, pp. 47-49. MR 1297773 (96e:26019)
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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:
10.1090/S0002-9939-05-08325-5
PII:
S 0002-9939(05)08325-5
Received by editor(s):
May 13, 2003
Received by editor(s) in revised form:
July 15, 2004
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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