An extension of Jörgens-Calabi-Pogorelov theorem to parabolic Monge-Ampère equation. (English) Zbl 1391.35250
Summary: We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge-Ampère equation to parabolic Monge-Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension \(n\geq 3\), the work of C. E. Gutiérrez and Q. Huang [Indiana Univ. Math. J. 47, No. 4, 1459–1480 (1998; Zbl 0926.35053)] is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge-Ampère equations.
MSC:
| 35K96 | Parabolic Monge-Ampère equations |
| 35B08 | Entire solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B53 | Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs |
Citations:
Zbl 0926.35053References:
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