Harnack inequality for the linearized parabolic monge-ampre equation

Transactions of the American Mathematical Society

Volumn 351, Issue 5, 1999, Pages 2025-2054

  Huang, Qingbo ^a,b  

^a Temple University   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Affine invariant; Harnack inequality; Linear parabolic monge amp re equation; Section

Indexed keywords

EID: 22644448903     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02142-x     Document Type: Article

References (14)

1. [Cal]L.A. Caffarelli, Some regularity properties of solutions of Mange-Ampere equation, Comm. Pure Appl. Math. XLIV (1991), 965-969. MR 92h:35088
2. Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. XLV (1992), 1141-1151. MR 93k:35054
3. [Ca-C] L. A. Caffarelli and X. Cabré, Fully nonlinear elliptic equations, AMS Colloquium Publications V. 43, AMS, Rhode Island, 1993. MR 96h:35046
4. [Ca-Gul] L. A. Caffarelli and C. E. Gutiérrez, Real analysis related to the Mange-Ampere equation, Trans. Amer. Math. Soc. 348 (1996), 1075-1092. MR 96h:35047
5. [Ca-Gu2] Properties of the solutions of the linearized Monge-Ampère equation, Amer. J. of Math. 119 (1997), 423-465. MR 98e:35060
6. [G-T] D. Gilbarg & N. S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, Springer-Verlag, 1983. MR 86c:35035
7. [Gu] C. E. Gutiérrez, On the Harnack inequality for viscosity solutions of non-divergence equations, preprint
8. [Gu-H] C. E. Gutiérrez & Q. Huang, Geometric properties of the sections of solutions of the Mange-Ampere equation, Trans. AMS. to appear
9. [K-S] N. V. Krylov & M. V. Safonov, Certain properties of solutions of parabolic equations with measurable coefficients, Izvestia Akad. Nauk. SSSR 44 (1980), 161-175. MR 83c:35059
10. [M] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure. Appl. Math. 17 (1964), 101-134. MR 28:2356
11. [S] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Math. Series #43, Princeton U. Press, Princeton, NJ, 1993. MR 95c:42002
12. [T] K. S. Tso, On an Alekandrov-Bakel'man type maximum principle for second-order parabolic equations, Comm. PDE 10 (1985), 543-553. MR 87f:35031
13. [W] L. Wang, On the regularity theory of fully nonlinear parabolic equations I, Comm. Pure Appl. Math. 45 (1992), 27-76. MR 92m:35126
14. [W-W] Rou-Huai Wang & Guang-Lie Wang, On existence, uniqueness and regularity of viscosity solutions for the first initial-boundary value problems to parabolic Mange-Ampere equation, Northeast. Math. J. 8 (1992), 417-446. MR 94d:35085