Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity

Zixiao Liu; Jiguang Bao

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arXiv · 2202.06461

Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity

Zixiao Liu·Jiguang Bao

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Abstract

We consider the asymptotic behavior of solutions to the Monge--Amp\`ere 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.

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BibTeX RIS

Zixiao Liu, Jiguang Bao. 2022-02-14. Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity. https://arxiv.org/abs/2202.06461

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