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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Symmetric decreasing rearrangement can be discontinuous

Authors: Frederick J. Almgren Jr. and Elliott H. Lieb
Journal: Bull. Amer. Math. Soc. 20 (1989), 177-180
MSC (1985): Primary 46E35; Secondary 26B99, 47B38
MathSciNet review: 968686
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  • J.-M. Coron, The continuity of the rearrangement in 𝑊^{1,𝑝}(𝑅), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 1, 57–85. MR 752580
  • Bernhard Kawohl, Rearrangements and convexity of level sets in PDE, Lecture Notes in Mathematics, vol. 1150, Springer-Verlag, Berlin, 1985. MR 810619
  • Elliott H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. (2) 118 (1983), no. 2, 349–374. MR 717827, 10.2307/2007032
  • G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, no. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486
  • Bernhard Ruf and Sergio Solimini, On a class of superlinear Sturm-Liouville problems with arbitrarily many solutions, SIAM J. Math. Anal. 17 (1986), no. 4, 761–771. MR 846387, 10.1137/0517055

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