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Asymptotic behavior of solutions to the Monge--Ampère equations with slow convergence rate at infinity

We consider the asymptotic behavior of solutions to the Monge--Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao--Li--Zhang [Calc. Var PDE. 52(2015). pp. 39-63]. Different from known results, we obtain the limit of Hessian and/or gradient of solution at infinity relying on the convergence rate. The basic idea is to use a revised level set method, the spherical harmonic expansion and the iteration method.

preprint2022arXivOpen access
Zixiao LiuJiguang Bao
math.AP
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Zixiao LiuJiguang Bao

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