The exterior Dirichlet problems of Monge–Ampère equations in dimension two
Keyword(s):
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.
2001 ◽
Vol 32
(3)
◽
pp. 201-209
◽
1995 ◽
Vol 58
(2)
◽
pp. 222-231
2018 ◽
Vol 2018
◽
pp. 1-10
◽
1982 ◽
Vol 19
(04)
◽
pp. 851-857
◽
2009 ◽
Vol 7
(3)
◽
pp. 209-223
◽
Keyword(s):