New isoperimetric estimates for solutions to Monge-Ampère equations

 Access to full text

 Full (PDF)

1. [1] Alvino A., Lions P.-L., Trombetti G., On optimization problems with prescribed rearrangements, Nonlinear Anal.13 (2) (1989) 185-220. Zbl0678.49003MR979040
2. [2] Alvino A., Lions P.-L., Trombetti G., Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire7 (2) (1990) 37-65. Zbl0703.35007MR1051227
3. [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. Zbl0633.53002MR936419
4. [4] Delanoë Ph., Radially symmetric boundary value problems for real and complex elliptic Monge–Ampère equations, J. Differential Equations58 (3) (1985) 318-344. Zbl0564.35044MR797314
5. [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. Zbl1147.58030MR2399068
6. [6] Kawohl B., Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Mathematics, vol. 1150, Springer-Verlag, Berlin, 1985. Zbl0593.35002MR810619
7. [7] Lions P.-L., Two remarks on Monge–Ampère equations, Ann. Mat. Pura Appl. (4)142 (1985) 263-275. Zbl0594.35023MR839040
8. [8] Lutwak E., On some affine isoperimetric inequalities, J. Differential Geom.23 (1) (1986) 1-13. Zbl0592.52005MR840399
9. [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. Zbl0576.52003MR809198
10. [10] Pólya G., Torsional rigidity, principal frequency, electrostatic capacity and symmetrization, Quart. Appl. Math.6 (1948) 267-277. Zbl0037.25301MR26817
11. [11] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, vol. 27, Princeton University Press, Princeton, NJ, 1951. Zbl0044.38301MR43486
12. [12] Reilly R.C., On the Hessian of a function and the curvatures of its graph, Michigan Math. J.20 (1973) 373-383. Zbl0267.53003MR334045
13. [13] Schneider R., Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. Zbl0798.52001MR1216521
14. [14] Talenti G., Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)3 (4) (1976) 697-718. Zbl0341.35031MR601601
15. [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. Zbl0467.35044MR623935
16. [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. Zbl0602.35025MR831299
17. [17] Talenti G., Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces, Ann. Mat. Pura Appl. (4)120 (1979) 160-184. Zbl0419.35041MR551065
18. [18] Trudinger N.S., On new isoperimetric inequalities and symmetrization, J. Reine Angew. Math.488 (1997) 203-220. Zbl0883.52006MR1465371
19. [19] Trudinger N.S., Wang X.J., A Poincaré type inequality for Hessian integrals, Calc. Var. Partial Differential Equations6 (4) (1998) 315-328. Zbl0927.58013MR1624292
20. [20] Tso K., On a real Monge–Ampère functional, Invent. Math.101 (2) (1990) 425-448. Zbl0724.35040MR1062970
21. [21] Tso K., Remarks on critical exponents for Hessian operators, Ann. Inst. H. Poincaré Anal. Non Linéaire7 (2) (1990) 113-122. Zbl0715.35031MR1051232
22. [22] Wang X.J., A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J.43 (1) (1994) 25-54. Zbl0805.35036MR1275451