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Bulletin of the American Mathematical Society

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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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  • 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,
  • [PS] G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. of Math. Studies no. 27, Princeton Univ. Press, Princeton, N. J., 1952. MR 43486
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