A generalization of a theorem by Calabi to the parabolic Monge-Ampère equation

Indiana University Mathematics Journal

Volumn 47, Issue 4, 1998, Pages 1459-1479

  Gutiérrez, Cristian E ^a   Huang, Qingbo ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040039956     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1998.47.1563     Document Type: Article

References (21)

1. A. D. ALEKSANDROV, Majorization of solutions of second-order linear equations, A. M. S. Transl. 2(68) (1968), 120-143.
2. 2,p estimates for solutions of the Monge-Ampère equation, Ann. of Math. 131 (1990), 135-150.
3. _, Boundary regularity of maps with convex potentials, Comm. on Pure and Appl. Math. 45 (1992), 1141-1151.
4. _, Monge-Ampère equation, div-curl theorems in Lagrangian coordinates, compression and rotation, lecture notes.
5. _ & X. CABRÉ, Fully Nonlinear Elliptic Equations, Colloquium Publications, vol. 43, A. M. S., Providence, R. I., 1995.
6. _ & C. E. GUTIÉRREZ, Properties of the solutions of the linearized Monge-Ampère equation, American J. of Math. 119(2) (1997), 423-465.
7. E. CALABI, Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Michigan Math. Jour. 5(2) (1958), 105-126.
8. S-Y. CHENG & S-T. YAU, Complete affine hypersurfaces, part I. The completeness of affine metrics, Comm. on Pure and App. Math. XXXIX (1986), 839-866.
9. C. E. GUTIÉRREZ & Q. HUANG, Geometric properties of the sections of solutions to the Monge-Ampère equation, to appear, Trans. A. M. S..
10. Q. HUANG, Harnack inequality for the linearized parabolic Monge-Ampère equation, to appear, Trans. A. M. S..
11. 2 = 1, Math. Ann. 127 (1954), 130-134.
12. N. V. KRYLOV, Nonlinear Elliptic and Parabolic Equations of Second Order, Mathematics and its Applications, Reidel, 1987.
13. _, Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation, Siberian Mat. J. 17 (1976), 226-236.
14. _ & M. V. SAFONOV, A certain property of solutions cf parabolic equations with measurable coefficients, Math. USSR Izvestija 16(1) (1931), 151-164.
15. O. A. LADYZHENSKAYA, V. A. SOLONNIKOV & N. N. URAL'TSEVA, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs 23, A. M. S., Providence R. I., 1968.
16. n) > 0, Soviet Math. Dokl. 12(5) (1971), 1436-1440.
17. _, On the improper convex affine hyperspheres, Geometriae Dedicata 1 (1972), 33-46.
18. _, The Minkowski Multidimensional Problem, John Wiley, Washington, D. C., 1978.
19. J. RAUCH & B. A. TAYLOR, The Dirichlet problem for the multidimensional Monge-Ampère equation, Rocky Mountain J. of Math. 7(2) (1977), 345-364.
20. KAISING TSO, Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure and Appl. Math. XXXVIII (1985), 867-882.
21. ROUHUAI WANG & GUANGLIE WANG, The geometric measure theoretical characterization of viscosity solutions to parabolic Monge-Ampère type equation, J. Partial Diff. Eqs. 6(3) (1993), 237-254.