Elliptic equations and rearrangements
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 3 (1976) no. 4, p. 697-718 
@article{ASNSP_1976_4_3_4_697_0,
     author = {Talenti, Giorgio},
     title = {Elliptic equations and rearrangements},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 3},
     number = {4},
     year = {1976},
     pages = {697-718},
     zbl = {0341.35031},
     mrnumber = {601601},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1976_4_3_4_697_0}
}

Talenti, Giorgio. Elliptic equations and rearrangements. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 3 (1976) no. 4, pp. 697-718. http://www.numdam.org/item/ASNSP_1976_4_3_4_697_0/

[1] G.A. Bliss, An integral inequality, J. London Math. Soc., 5 (1930). | JFM 56.0434.02

[2] H. Federer - W.H. Fleming, Normal and integral currents, Annals of Math., 72 (1960). | MR 123260 | Zbl 0187.31301

[3] W. Fleming - R. Rishel, An integral formula for total gradient variation, Arch. Math., 11 (1960). | MR 114892 | Zbl 0094.26301

[4] F.W. Gehring, Symmetrization of rings in space, Trans. Amer. Math. Soc., 101 (1961). | MR 132841 | Zbl 0104.30002

[5] E. De Giorgi, Su una teoria generale della misura (r -1) dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl., 36 (1954). | MR 62214 | Zbl 0055.28504

[6] G.H. Hardy - J.E. Littlewood - G. Polya, Inequalities, Cambridge Univ. Press (1964).

[7] W.K. Hayman, Multivalent functions, Cambridge Univ. Press (1958). | MR 108586 | Zbl 0082.06102

[8] O.A. Ladyzenskaja - N.N. Ural'Ceva, Linear and quasilinear equations of elliptic type, Isdat. Nauka, Moscow (1964). | MR 509265 | Zbl 0143.33602

[9] C. Miranda, Partial differential equations of elliptic type, Springer Verlag (1970). | MR 284700 | Zbl 0198.14101

[10] D.S. Mitrinovic, Analytic inequalities, Springer Verlag (1970). | MR 274686 | Zbl 0199.38101

[11] R. O'Neil, Convolution operators and L(p, q) spaces, Duke Math. J., 30 (1963). | Zbl 0178.47701

[12] R. O'Neil, Integral transforms and tensor products on Orlicz spaces and L(p, q) spaces, Journal Analyse Math., 21 (1968). | MR 626853 | Zbl 0182.16703

[13] L.E. Payne, Isoperimetric inequalities and their applications, SIAM Review, 9 (1967). | MR 218975 | Zbl 0154.12602

[14] L.E. Payne - M.E. Rayner, Some isoperimetric norm bounds for solutions of the Helmotz equation, Z. Angew. Math. Phys., 24 (1973). | MR 324202 | Zbl 0256.35023

[15] G. Polya - G. Szegö, Isoperimetric inequalities in Mathematical Physics, Ann. of Math. Stucies, No. 27, Princeton (1951). | MR 43486 | Zbl 0044.38301

[16] J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa, 18 (1964). | Numdam | MR 170094 | Zbl 0142.37601

[17] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Grenoble, 15 (1965). | Numdam | MR 192177 | Zbl 0151.15401

[18] G. Stampacchia, Regularisation des solutions de problèmes aux limites elliptiques à données discontinues, Proceedings of the international Symposium on linear spaces, Jerusalem (1960). | MR 146512 | Zbl 0114.30403

[19] S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, New Jersey (1964). | MR 193578 | Zbl 0129.13102

[20] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., to appear. | MR 463908 | Zbl 0353.46018

[21] H.F. Weinberger, Symmetrization in uniformly elliptic problems, Studies in Math. Anal., Stanford Univ. Press (1962). | MR 145191 | Zbl 0123.07202