@article{AIHPC_2006__23_4_539_0, author = {Van Schaftingen, Jean}, title = {Anisotropic symmetrization}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {23}, year = {2006}, pages = {539-565}, doi = {10.1016/j.anihpc.2005.06.001}, mrnumber = {2245755}, zbl = {05060816}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_4_539_0} }
Van Schaftingen, Jean. Anisotropic symmetrization. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 539-565. doi : 10.1016/j.anihpc.2005.06.001. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_4_539_0/
[1] Sobolev Spaces, Pure Appl. Math., vol. 65, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030
,[2] Convex symmetrization and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (2) (1997) 275-293. | Numdam | MR 1441395 | Zbl 0877.35040
, , , ,[3] On optimization problems with prescribed rearrangements, Nonlinear Anal. 13 (2) (1989) 185-220. | MR 979040 | Zbl 0678.49003
, , ,[4] A unified approach to symmetrization, in: , (Eds.), Partial Equations of Elliptic Type, Sympos. Math., vol. 35, Cambridge University Press, Cambridge, 1995, pp. 47-49. | MR 1297773 | Zbl 0830.35005
,[5] A general rearrangement inequality for multiple integrals, J. Funct. Anal. 17 (1974) 227-237. | MR 346109 | Zbl 0286.26005
, , ,[6] An approach to symmetrization via polarization, Trans. Amer. Math. Soc. 352 (4) (2000) 1759-1796. | MR 1695019 | Zbl 0965.49001
, ,[7] Cases of equality in the Riesz rearrangement inequality, Ann. of Math. (2) 143 (3) (1996) 499-527. | MR 1394967 | Zbl 0876.26016
,[8] Steiner symmetrization is continuous in , Geom. Funct. Anal. 7 (5) (1997) 823-860. | MR 1475547 | Zbl 0912.46034
,[9] The isoperimetric problem for Minkowski area, Amer. J. Math. 71 (1949) 743-762. | MR 31762 | Zbl 0038.10301
,[10] Rearrangements of functions, J. Funct. Anal. 66 (1986) 432-438. | MR 839110 | Zbl 0612.46027
, , ,[11] Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. | MR 990890 | Zbl 0703.49001
,[12] Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) 71 (2) (1992) 97-118. | MR 1170247 | Zbl 0676.46031
, ,[13] Convex Analysis and Variational Problems, Stud. Math. Appl., vol. 1, North-Holland Publishing Co., Amsterdam, 1976. | MR 463994 | Zbl 0322.90046
, ,[14] Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR 257325 | Zbl 0176.00801
,[15] A uniqueness proof for the Wulff theorem, Proc. Roy. Soc. Edinburgh Sect. A 119 (1-2) (1991) 125-136. | MR 1130601 | Zbl 0752.49019
, ,[16] On the shape of solutions to some variational problems, in: Nonlinear Analysis, Function Spaces and Applications, vol. 5, Prague, 1994, Prometheus, Prague, 1994, pp. 77-102. | MR 1322310 | Zbl 0841.49022
,[17] Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., vol. 1150, Springer-Verlag, Berlin, 1985. | MR 810619 | Zbl 0593.35002
,[18] On the symmetrization of anisotropic integral functionals, Izv. Vyssh. Uchebn. Zaved. Mat. (8) (1999) 26-32. | MR 1730536 | Zbl 1011.31003
,[19] Analysis, Grad. Stud. Math., vol. 14, American Mathematical Society, Providence, RI, 2001. | MR 1817225 | Zbl 0966.26002
, ,[20] Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (3) (1982) 315-334. | MR 683027 | Zbl 0501.46032
,[21] Inégalités isopérimétriques et applications en physique, Travaux en cours, Hermann, Paris, 1984. | MR 733257 | Zbl 0537.35002
,[22] Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ, 1951. | MR 43486 | Zbl 0044.38301
, ,[23] Symmetrization of condensers in n-space, Ann. Acad. Sci. Fenn., Ser. A I 522 (1972) 1-44. | MR 348108 | Zbl 0245.30013
,[24] Probability for Analysts, Chapman & Hall Probability Series, Chapman & Hall, New York, 1994, Lecture notes prepared by Kuppusamy Ravindran. | MR 1271144 | Zbl 0803.60001
,[25] Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976) 353-372. | MR 463908 | Zbl 0353.46018
,[26] On isoperimetric theorems of mathematical physics, in: , (Eds.), Handbook of Convex Geometry B, Elsevier Science, Amsterdam, 1993, pp. 1131-1147. | MR 1243005 | Zbl 0804.35005
,[27] Crystalline variational problems, Bull. Amer. Math. Soc. 84 (4) (1978) 568-588. | MR 493671 | Zbl 0392.49022
,[28] Universal approximation of symmetrizations by polarizations, Proc. Amer. Math. Soc. 134 (1) (2006) 177-186. | MR 2170557 | Zbl 1093.26012
,[29] Set transformations, symmetrizations and isoperimetric inequalities, in: , (Eds.), Nonlinear Analysis and Applications to the Physical Sciences, Springer, 2004, pp. 135-152. | MR 2085832
, ,[30] Analyse fonctionnelle élémentaire, Cassini, Paris, 2003. | Zbl 1089.46001
,[31] Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation, Grad. Texts in Math., vol. 120, Springer-Verlag, New York, 1989. | MR 1014685 | Zbl 0692.46022
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