Stability of Bernstein type theorem for the minimal surface equation

2022/01/17 by Guosheng Jiang, Jiang, Guosheng, Zhehui Wang +3
Computer Science · Mathematics · #35A09 #35B50 #35B53 #35J93 #53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2201.06443

openalex publication_date 2022/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω\subsetneq Rⁿ (n≥ 2) be an unbounded convex domain. We study the minimal surface equation in Ω with boundary value given by the sum of a linear function and a bounded uniformly continuous function in Rⁿ. If Ω is not a half space, we prove that the solution is unique. If Ω is a half space, we prove that graphs of all solutions form a foliation of Ω\timesR. This can be viewed as a stability type theorem for Edelen-Wang's Bernstein type theorem in \citeEW2021. We also establish a comparison principle for the minimal surface equation in Ω.

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