Properties of the solutions of the linearized Monge-Ampère equation

American Journal of Mathematics

Volumn 119, Issue 2, 1997, Pages 423-465

  Caffarelli, Luis A ^b   Gutiérrez, Cristian E ^a  

^a Temple University   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001041533     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. A. D. Aleksandrov, Majorization of solutions of second-order linear equations, Amer. Math. Soc. Transl. Ser. 2, vol. 68, Amer. Math. Soc., Providence, RI, 1968, pp. 120-143.
2. Y. Brenier, Décomposition Polaire et Réarrangement des Champs de Vecteurs, C. R. Acad. Sci. Paris Série 1 Math. I (1987), 805-808.
3. L. A. Caffarelli, Interior apriori estimates for solutions of fully non-linear equations, Ann. Math. 130 (1989), 189-213.
4. _, Some regularity properties of solutions of Monge-Ampère equation, Comm. Pure Appl. Math. XLIV (1991), 965-969.
5. _, Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. XLV (1992), 1141-1151.
6. L. A. Caffarelli and C. E. Gutiérrez, Real analysis related to the Monge-Ampère equation, Trans. Amer. Math. Soc. 348 (1996), 1075-1092.
7. L. A. Caffarelli, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations I. Monge-Ampère equation, Comm. Pure Appl. Math. XXXVII (1984), 369-402.
8. M. J. P. Cullen, J. Norbury, and R. J. Purser, Generalised Lagrangian solutions for atmospheric and oceanic flows, SIAM J. Appl. Math. 5 (1991), 20-31.
9. D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1983.
10. C. E. Gutiérrez, On the Harnack inequality for viscosity solutions of non-divergence equations, preprint.
11. C. E. Gutiérrez and Q. Huang, Geometric properties of the sections of solutions of the Monge-Ampère equation, preprint.
12. Q. Huang, Harnack inequality for the linearized parabolic Monge-Ampère equation, preprint.
13. E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Series, no. 43, Princeton Univ. Press, Princeton, NJ, 1993.