Convergence of an iterative scheme for the Monge-Amp\`ere eigenvalue problem with general initial data
Analysis of PDEs
2025-11-18 v4
Abstract
In this note, we revisit an iterative scheme, due to Abedin and Kitagawa (Inverse Iteration for the Monge-Amp\`ere Eigenvalue Problem, Proc. Amer. Math. Soc. 148 (2020), no. 11, 4875--4886), to solve the Monge-Amp\`ere 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-Amp\`ere eigenfunction. As an application, we obtain an energy characterization of the Monge--Amp\`ere eigenfunctions.
Keywords
Cite
@article{arxiv.2006.06564,
title = {Convergence of an iterative scheme for the Monge-Amp\`ere eigenvalue problem with general initial data},
author = {Nam Q. Le},
journal= {arXiv preprint arXiv:2006.06564},
year = {2025}
}
Comments
v4: Question 5.1 is now completely answered in Theorem 1.8; to be published in Advances in Continuous and Discrete Models: Theory and Applications