Asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity
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Publication:6391017
DOI10.1515/ANS-2022-0052arXiv2202.06461MaRDI QIDQ6391017
Publication date: 13 February 2022
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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