Abstract
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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