AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$
det
D
2
u
=
f
in dimension two with f being a perturbation of $f_{0}$
f
0
at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.
AbstractIn this paper, we study the Cauchy problem of the parabolic Monge–Ampère
equation-u_{t}\det D^{2}u=f(x,t)and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.
In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations det D 2 u = f ( x ) .
The exterior Dirichlet problems of Monge–Ampère equations in dimension two
