Boundary blow-up solutions to real (N-1)-Monge-Ampère equations with singular weights

2025/11/15 by Kiran Kumar Saha, Saha, Kiran Kumar, Sweta Tiwari +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2511.12091

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a boundary blow-up problem for real (N-1)-Monge-Ampère equations of the form \ \beginaligned amp; det^(1)/(N-1)(ΔzI-D²z)=K(|x|)f(z) amp;amp; in Ω, amp; z(x) → ∞ as \dist(x,∂Ω) → 0, \endaligned . where Ω denotes a ball in ℝ^N ~ (N ≥ 2). The weight function K is allowed to be singular, and the nonlinearity f is assumed to satisfy a Keller-Osserman type condition. We establish the existence of infinitely many radial (N-1)-convex solutions to the system by employing the method of sub- and super-solutions, in conjunction with a comparison principle.

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