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arXiv · 2006.06564

Convergence of an iterative scheme for the Monge-Amp\`ere eigenvalue problem with general initial data

Nam Q. Le
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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.

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Nam Q. Le. 2020-06-11. Convergence of an iterative scheme for the Monge-Amp\`ere eigenvalue problem with general initial data. https://arxiv.org/abs/2006.06564

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