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<p>In this note, we revisit an iterative scheme, due to Abedin and Kitagawa (Proc. Am. Math. Soc. 148:4875–4886, <CitationRef CitationID="CR1">2020</CitationRef>), to solve the Monge–Ampère eigenvalue problem on a general bounded convex domain. Using a nonlinear integration by parts, we show that the scheme converges for all convex initial data having finite and nonzero Rayleigh quotient to a nonzero Monge–Ampère eigenfunction. As an application, we obtain an energy characterization of the Monge–Ampère eigenfunctions.</p>

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Convergence of an iterative scheme for the Monge–Ampère eigenvalue problem with general initial data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月28日

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  • Nam Q. Le

摘要

In this note, we revisit an iterative scheme, due to Abedin and Kitagawa (Proc. Am. Math. Soc. 148:4875–4886, 2020), to solve the Monge–Ampère eigenvalue problem on a general bounded convex domain. Using a nonlinear integration by parts, we show that the scheme converges for all convex initial data having finite and nonzero Rayleigh quotient to a nonzero Monge–Ampère eigenfunction. As an application, we obtain an energy characterization of the Monge–Ampère eigenfunctions.