Anisotropic symmetrization

Van Schaftingen, Jean

doi:10.1016/j.anihpc.2005.06.001

Van Schaftingen, Jean

Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 539-565.

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2005.06.001

@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},
     pages = {539--565},
     publisher = {Elsevier},
     volume = {23},
     number = {4},
     year = {2006},
     doi = {10.1016/j.anihpc.2005.06.001},
     mrnumber = {2245755},
     zbl = {05060816},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2005.06.001/}
}

TY  - JOUR
AU  - Van Schaftingen, Jean
TI  - Anisotropic symmetrization
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2006
SP  - 539
EP  - 565
VL  - 23
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2005.06.001/
DO  - 10.1016/j.anihpc.2005.06.001
LA  - en
ID  - AIHPC_2006__23_4_539_0
ER  -

%0 Journal Article
%A Van Schaftingen, Jean
%T Anisotropic symmetrization
%J Annales de l'I.H.P. Analyse non linéaire
%D 2006
%P 539-565
%V 23
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2005.06.001/
%R 10.1016/j.anihpc.2005.06.001
%G en
%F AIHPC_2006__23_4_539_0

Van Schaftingen, Jean. Anisotropic symmetrization. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 539-565. doi : 10.1016/j.anihpc.2005.06.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2005.06.001/

Bibliographie
Cité par

[1] Adams R.A., Sobolev Spaces, Pure Appl. Math., vol. 65, Academic Press, New York, 1975. | MR | Zbl

[2] Alvino A., Ferone V., Trombetti G., Lions P.-L., Convex symmetrization and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (2) (1997) 275-293. | Numdam | MR | Zbl

[3] Alvino A., Trombetti G., Lions P.-L., On optimization problems with prescribed rearrangements, Nonlinear Anal. 13 (2) (1989) 185-220. | MR | Zbl

[4] Baernstein A., A unified approach to symmetrization, in: Alvino A., (Eds.), Partial Equations of Elliptic Type, Sympos. Math., vol. 35, Cambridge University Press, Cambridge, 1995, pp. 47-49. | MR | Zbl

[5] Brascamp H.J., Lieb E.H., Luttinger J.M., A general rearrangement inequality for multiple integrals, J. Funct. Anal. 17 (1974) 227-237. | MR | Zbl

[6] Brock F., Solynin A.Yu., An approach to symmetrization via polarization, Trans. Amer. Math. Soc. 352 (4) (2000) 1759-1796. | MR | Zbl

[7] Burchard A., Cases of equality in the Riesz rearrangement inequality, Ann. of Math. (2) 143 (3) (1996) 499-527. | MR | Zbl

[8] Burchard A., Steiner symmetrization is continuous in $W^{1, p}$ , Geom. Funct. Anal. 7 (5) (1997) 823-860. | MR | Zbl

[9] Busemann H., The isoperimetric problem for Minkowski area, Amer. J. Math. 71 (1949) 743-762. | MR | Zbl

[10] Crowe J.A., Rosenbloom P.C., Zweibel J.A., Rearrangements of functions, J. Funct. Anal. 66 (1986) 432-438. | MR | Zbl

[11] Dacorogna B., Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. | MR | Zbl

[12] Dacorogna B., Pfister C.-E., Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) 71 (2) (1992) 97-118. | MR | Zbl

[13] Ekeland I., Temam R., Convex Analysis and Variational Problems, Stud. Math. Appl., vol. 1, North-Holland Publishing Co., Amsterdam, 1976. | MR | Zbl

[14] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR | Zbl

[15] Fonseca I., Müller S., A uniqueness proof for the Wulff theorem, Proc. Roy. Soc. Edinburgh Sect. A 119 (1-2) (1991) 125-136. | MR | Zbl

[16] Kawohl B., 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 | Zbl

[17] Kawohl B., Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., vol. 1150, Springer-Verlag, Berlin, 1985. | MR | Zbl

[18] Klimov V.S., On the symmetrization of anisotropic integral functionals, Izv. Vyssh. Uchebn. Zaved. Mat. (8) (1999) 26-32. | MR | Zbl

[19] Lieb E.H., Loss M., Analysis, Grad. Stud. Math., vol. 14, American Mathematical Society, Providence, RI, 2001. | MR | Zbl

[20] Lions P.-L., Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (3) (1982) 315-334. | MR | Zbl

[21] Mossino J., Inégalités isopérimétriques et applications en physique, Travaux en cours, Hermann, Paris, 1984. | MR | Zbl

[22] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ, 1951. | MR | Zbl

[23] Sarvas J., Symmetrization of condensers in n-space, Ann. Acad. Sci. Fenn., Ser. A I 522 (1972) 1-44. | MR | Zbl

[24] Stromberg K.R., Probability for Analysts, Chapman & Hall Probability Series, Chapman & Hall, New York, 1994, Lecture notes prepared by Kuppusamy Ravindran. | MR | Zbl

[25] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976) 353-372. | MR | Zbl

[26] Talenti G., On isoperimetric theorems of mathematical physics, in: Gruber P.M., Wills J. (Eds.), Handbook of Convex Geometry B, Elsevier Science, Amsterdam, 1993, pp. 1131-1147. | MR | Zbl

[27] Taylor J.E., Crystalline variational problems, Bull. Amer. Math. Soc. 84 (4) (1978) 568-588. | MR | Zbl

[28] Van Schaftingen J., Universal approximation of symmetrizations by polarizations, Proc. Amer. Math. Soc. 134 (1) (2006) 177-186. | MR | Zbl

[29] Van Schaftingen J., Willem M., Set transformations, symmetrizations and isoperimetric inequalities, in: Benci V., Masiello A. (Eds.), Nonlinear Analysis and Applications to the Physical Sciences, Springer, 2004, pp. 135-152. | MR

[30] Willem M., Analyse fonctionnelle élémentaire, Cassini, Paris, 2003. | Zbl

[31] Ziemer W.P., Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation, Grad. Texts in Math., vol. 120, Springer-Verlag, New York, 1989. | MR | Zbl

Cité par Sources :