Convex symmetrization and applications
Alvino, Angelo ; Ferone, Vincenzo ; Trombetti, Guido ; Lions, Pierre-Louis
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 275-293 / Harvested from Numdam
@article{AIHPC_1997__14_2_275_0,
     author = {Alvino, Angelo and Ferone, Vincenzo and Trombetti, Guido and Lions, Pierre-Louis},
     title = {Convex symmetrization and applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {275-293},
     mrnumber = {1441395},
     zbl = {0877.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_2_275_0}
}
Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido; Lions, Pierre-Louis. Convex symmetrization and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 275-293. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_2_275_0/

[ADLT] A. Alvino, J.I. Díaz, P.-L. Lions and G. Trombetti, Elliptic equations and Steiner symmetrization, C.R. Acad. Sci. Paris, Vol. 314, 1992, pp. 1015-1020. | MR 1168527 | Zbl 0795.35022

[ALT] A. Alvino, P.-L. Lions and G. Trombetti, Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. Inst. Henri Poinearé, Analyse Nonlineaire, Vol. 7, 1990, pp. 37-65. | Numdam | MR 1051227 | Zbl 0703.35007

[AB] M. Amar and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients, Ann. Inst. Henri Poincaré, Analyse Nonlineaire, Vol. 11, 1994, pp. 91-133. | Numdam | MR 1259102 | Zbl 0842.49016

[Ba] C. Bandle, On symmetrizations in parabolic equations, J. Anal. Math., Vol. 30, 1976, pp. 98-112. | MR 442477 | Zbl 0331.35036

[BFM] M.F. Betta, V. Ferone and A. Mercaldo, Regularity for solutions of nonlinear elliptic equations, Bull. Sci. Math., Vol. 118, 1994, pp. 539-567. | MR 1309088 | Zbl 0842.35014

[BZ] Yu.D. Burago and V.A. Zalgaller, Geometric Inequalities, Springer-Verlag, Berlin, 1988. | MR 936419 | Zbl 0633.53002

[Bu] H. Buseman, The isoperimetric problem for Minkowski area, Amer. J. Math., Vol. 71, 1949, pp. 743-762. | MR 31762 | Zbl 0038.10301

[DG] E. De Giorgi, Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura e Appl., Vol. 36, 1954, pp. 191-213. | MR 62214 | Zbl 0055.28504

[FP] V. Ferone and M.R. Posteraro, Symmetrization results for elliptic equations with lower-order terms, Atti Sem. Mat. Fis. Univ. Modena, Vol. 39, 1991, pp. 47-61. | MR 1179021 | Zbl 0796.35034

[FPV] V. Ferone, M.R. Posteraro and R. Volpicelli, An inequality concerning rearrangements of functions and Hamilton-Jacobi equations, Arch. Rat. Mech. Anal., Vol. 125, 1993, pp. 257-269. | MR 1245072 | Zbl 0787.35020

[GN] E. Giarrusso and D. Nunziante, Symmetrization in a class of first-order Hamilton-Jacobi equations, Nonlinear Analysis T.M.A., Vol. 8, 1984, pp. 289-299. | MR 739660 | Zbl 0543.35014

[G] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel, 1984. | MR 775682 | Zbl 0545.49018

[La] S.R. Lay, Convex sets and their applications, J. Wiley and Sons, New York, 1982. | MR 655598 | Zbl 0492.52001

[Li] P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. | MR 667669 | Zbl 0497.35001

[M] V.G. Maz'Ja, Sobolev spaces, Springer-Verlag, Berlin, 1985. | MR 817985

[MR] J. Mossino and J.M. Rakotoson, Isoperimetric inequalities in parabolic equations, Ann. Scuola Norm. Sup. Pisa, Vol. 13, 1986, pp. 51-73. | Numdam | MR 863635 | Zbl 0652.35053

[PS] G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. Math. Studies, No. 27, Princeton University Press, Princeton, 1951. | MR 43486 | Zbl 0044.38301

[R] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. | MR 274683 | Zbl 0193.18401

[T1] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura e Appl., Vol. 110, 1976, pp. 353-372. | MR 463908 | Zbl 0353.46018

[T2] G. Talenti, Elliptic Equations and Rearrangements, Ann. Scuola Norm. Sup. Pisa, (4) Vol. 3, 1976, pp. 697-718. | Numdam | MR 601601 | Zbl 0341.35031

[T3] G. Talenti, Nonlinear elliptic equations, rearrangements of function and Orlicz spaces, Ann. Mat. Pura Appl., (4) Vol. 120, 1979, pp. 159-184. | MR 551065 | Zbl 0419.35041