Work

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

Year: 2025

Type: article

Abstract: 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.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-025-04037-0

Author: Nam Q. Le

Institutions: Indiana University Bloomington, Indiana University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,890

Funder: Directorate for Mathematical and Physical Sciences