no. 4
New Isoperimetric Estimates for Solutions to Monge-Ampère Equations
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1265-1275. 
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     author = {Brandolini, B. and Nitsch, C. and Trombetti, C.},
     title = {New {Isoperimetric} {Estimates} for {Solutions} to {Monge-Amp\`ere} {Equations}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1265--1275},
     publisher = {Elsevier},
     volume = {26},
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     year = {2009},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.005/}
}
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Brandolini, B.; Nitsch, C.; Trombetti, C. New Isoperimetric Estimates for Solutions to Monge-Ampère Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1265-1275. doi : 10.1016/j.anihpc.2008.09.005. http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.005/

[1] Alvino A., Lions P.-L., Trombetti G., On Optimization Problems With Prescribed Rearrangements, Nonlinear Anal. 13 (2) (1989) 185-220. | MR | Zbl

[2] Alvino A., Lions P.-L., Trombetti G., Comparison Results for Elliptic and Parabolic Equations Via Schwarz Symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (2) (1990) 37-65. | Numdam | MR | Zbl

[3] Burago Yu. D., Zalgaller V. A., Geometric Inequalities, Grundlehren der Mathematischen Wissenschaften, vol. 285, Springer-Verlag, Berlin, 1988, Translated from the Russian by A.B. Sosinskiĭ, Springer Series in Soviet Mathematics. | MR | Zbl

[4] Delanoë Ph., Radially Symmetric Boundary Value Problems for Real and Complex Elliptic Monge-Ampère Equations, J. Differential Equations 58 (3) (1985) 318-344. | MR | Zbl

[5] Freitas P., Krejčiřík D., A Sharp Upper Bound for the First Dirichlet Eigenvalue and the Growth of the Isoperimetric Constant of Convex Domains, Proc. Amer. Math. Soc. 136 (8) (2008) 2997-3006. | MR | Zbl

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

[7] Lions P.-L., Two Remarks on Monge-Ampère Equations, Ann. Mat. Pura Appl. (4) 142 (1985) 263-275. | MR | Zbl

[8] Lutwak E., On Some Affine Isoperimetric Inequalities, J. Differential Geom. 23 (1) (1986) 1-13. | MR | Zbl

[9] Petty C. M., Affine Isoperimetric Problems, in: Discrete Geometry and Convexity, New York, 1982, Ann. New York Acad. Sci., vol. 440, New York Acad. Sci., New York, 1985, pp. 113-127. | MR | Zbl

[10] Pólya G., Torsional Rigidity, Principal Frequency, Electrostatic Capacity and Symmetrization, Quart. Appl. Math. 6 (1948) 267-277. | MR | Zbl

[11] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, vol. 27, Princeton University Press, Princeton, NJ, 1951. | MR | Zbl

[12] Reilly R. C., On the Hessian of a Function and the Curvatures of Its Graph, Michigan Math. J. 20 (1973) 373-383. | MR | Zbl

[13] Schneider R., Convex Bodies: the Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. | MR | Zbl

[14] Talenti G., Elliptic Equations and Rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (4) (1976) 697-718. | Numdam | MR | Zbl

[15] Talenti G., Some Estimates of Solutions to Monge-Ampère Type Equations in Dimension Two, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (2) (1981) 183-230. | Numdam | MR | Zbl

[16] Talenti G., Linear Elliptic P.D.E.'s: Level Sets, Rearrangements and a Priori Estimates of Solutions, Boll. Un. Mat. Ital. B (6) 4 (3) (1985) 917-949. | MR | Zbl

[17] Talenti G., Nonlinear Elliptic Equations, Rearrangements of Functions and Orlicz Spaces, Ann. Mat. Pura Appl. (4) 120 (1979) 160-184. | MR | Zbl

[18] Trudinger N. S., On New Isoperimetric Inequalities and Symmetrization, J. Reine Angew. Math. 488 (1997) 203-220. | MR | Zbl

[19] Trudinger N. S., Wang X. J., A Poincaré Type Inequality for Hessian Integrals, Calc. Var. Partial Differential Equations 6 (4) (1998) 315-328. | MR | Zbl

[20] Tso K., On a Real Monge-Ampère Functional, Invent. Math. 101 (2) (1990) 425-448. | MR | Zbl

[21] Tso K., Remarks on Critical Exponents for Hessian Operators, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (2) (1990) 113-122. | Numdam | MR | Zbl

[22] Wang X. J., A Class of Fully Nonlinear Elliptic Equations and Related Functionals, Indiana Univ. Math. J. 43 (1) (1994) 25-54. | MR | Zbl

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