A Liouville theorem of parabolic Monge-Ampère equations in half-space. (English) Zbl 1458.35249
Summary: In this paper, we establish the gradient and second derivative estimates for solutions to two kinds of parabolic Monge-Ampère equations in half-space under certain boundary data and growth condition. We also use such estimates to obtain the Liouville theorems for these two kinds of parabolic Monge-Ampère equations and one kind of elliptic Monge-Ampère equation.
MSC:
| 35K96 | Parabolic Monge-Ampère equations |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35B53 | Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs |
| 35B45 | A priori estimates in context of PDEs |
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