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## Abstract In this paper, we study the parabolic Monge–Ampère equations $-u\_{t}\det (D^{2}u)=g$ − u t det ( D 2 u ) = g outside a bowl-shaped domain with g being the perturbation of $g\_{0}(|x|)$ g 0 ( | x | ) at infinity. Under the weaker conditions compared with the problem outside a cylinder, we obtain the existence and uniqueness of viscosity solutions with asymptotic behavior for the first initial-boundary value problem by using the Perron method.

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Author

Limei Dai; Huihui Cheng

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Mathematics (Physical Sciences)