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