Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity
Analysis of PDEs
2022-02-15 v1
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.
Keywords
Cite
@article{arxiv.2202.06461,
title = {Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity},
author = {Zixiao Liu and Jiguang Bao},
journal= {arXiv preprint arXiv:2202.06461},
year = {2022}
}
Comments
22 pages