Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-09T09:34:49.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetrization and currents

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Emanuel Sperner Jr
Emanuel Sperner Jr
Affiliation:
Fachbereich Mathematik und Physik, der Universität Bayreuth, Postfach 3008, D-8580 Bayreuth, Federal Republik of Germany
Get access

Extract

Recently the notion of elementary symmetrization attracted new attention in the field of convex sets (see [L; W]), and it was proved that Minkowski's “Quermassintegrale” are decreased by elementary symmetrization. On the other hand, the concept of Schwarz symmetrization for Borel functions gained new interest from its possible applications in the field of elliptic partial differential equations (see [S1, S2, HI, T1, T2, HY1, HY2, GL1, GL2]).

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 26 , Issue 2 , December 1979 , pp. 269 - 289
Copyright
Copyright © University College London 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

B.Bauer, H.. Wahrscheinlichkeitstheorie (Berlin, 1974).Google Scholar
D1.Dinghas, A.. Minkowskische Summen und Integrate (Paris, 1961).Google Scholar
D2.Dinghas, A.. “Über das Verhalten der Entfernung zweier Punktmengen bei gleichzeitiger Symmetrisierung derselben”, Arch. Math. 8 (1957), 46–51.CrossRefGoogle Scholar
DG.DeGiorgi, E.. “Sulla proprieta isoperimetrica dell'ipersfera, nelle classe degli insiemi aventi frontiera orientata di misura finita”, Memorie Ace. Naz. Lincei, Ser. 8, 5 (1958), 33–44.Google Scholar
F.Federer, H.. Geometric Measure Theory (New York, 1969).Google Scholar
GL1.Gariepy, R. and Lewis, J.. “A maximum principle with applications to subharmonic functions in nspace”, Arkivf. Mat., 12 (1974), 253–266.CrossRefGoogle Scholar
GL2.Gariepy, R. and Lewis, J.. “Space analogues of some theorems for subharmonic and meromorphic functions”, Arkivf. Mat., 13 (1975), 91–105.CrossRefGoogle Scholar
H.Hadwiger, H.. Vorlesungen lifter Inhalt, Oberflache und Isoperimetrie (Berlin, 1957).CrossRefGoogle Scholar
HA.Haupt, O. and Aumann, G.. Differential- und Integratrechnung I (Berlin, 1934).Google Scholar
HI.Hildén, K.. “Symmetrization of Functions in Sobolev Spaces and the Isoperimetric Inequality”, Man. Mat., 18 (1976), 215–235.CrossRefGoogle Scholar
HY1.Friedland, S. and Hayman, W. K.. “Eigenvalue Inequalities for the Dirichlet Problem on Spheres and the Growth of Subharmonic Functions”, Comment. Math. Helvetici, 51 (1976), 133–161.CrossRefGoogle Scholar
HY2.Hayman, W. K.. “Some Bounds for Principal Frequency”, Appl. Anal., 7 (1978), 247–254.CrossRefGoogle Scholar
L.Leichtweiss, K.. “Bemerkungen zur Symmetrisierung an Unterraumen des euklidischen Raumes”, Arch. Math., 30 (1978), 541–550.CrossRefGoogle Scholar
N.Nečas, J.. Équations Elliptiques (Paris, 1967).Google Scholar
S1.JrSperner, E.. “Symmetrisierung fur Funktionen mehrerer reeller Variablen”, Man. Mat., 11 (1974), 159–170.CrossRefGoogle Scholar
S2.JrSperner, E.. “Zur Symmetrisierung von Funktionen auf Sphären”. Math. Zeit., 134 (1973), 317–327.CrossRefGoogle Scholar
S3.JrSperner, E.. “Partielle Differentialgleichungen in singularen Gebieten”, to appear.Google Scholar
Tl.Talenti, G.. “Best constant in Sobolev inequality”, Annali Mat. pur. et appl., 110 (1976), 353–372.CrossRefGoogle Scholar
T2.Talenti, G.. “Nonlinear Elliptic Equations, Rearrangement of Functions and Orlicz spaces”, Appl. Anal., 6 (1977), 317–318.CrossRefGoogle Scholar
W.Wills, J.. “Symmetrisierung an Unterräumen”, Arch. Math., 20 (1969), 169–172.CrossRefGoogle Scholar
Z.Zaanen, A.. An Introduction to the Theory of Integration (Amsterdam, 1965).Google Scholar