Exterior problems for more general parabolic Monge–Ampère equation in more general domain

In this paper, we consider the exterior problem for more general parabolic Monge–Ampère equation ut=ρ(logdet(D2u))ut=ρ(logdet(D2u)) in more general domain RT1,2n+1\D, RT1,2n+1=Rn+1×(−T1,T2], D=Ω×(−T1,T2)D=Ω×(−T1,T2). Using the Perron method, we obtain the existence and uniqueness of viscosity solution with asymptotic behavior at infinity. The results of exterior problems for the parabolic Monge–Ampère equation ut−logdet(D2u)=1ut−logdet(D2u)=1 are extended.