The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

Abstract

AbstractIn 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.