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arXiv · 2609.12630

Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary

Guofang Wang·Wei Wei·Chao Xia·Xuwen Zhang
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Abstract

In this paper, we continue our recent study on anisotropic minimal surface equation with free boundary condition in Wang-Wei-Xia-Zhang (Arch Ration Mech Anal 250:42, 2026). The first main result solves the corresponding mixed boundary value problem. As an application, we prove the following Bernstein-type theorem: any anisotropic minimal graph over $\mathbb{R}^3_+$ with free boundary must be flat. These extend the classical results of Simon (Indiana Univ Math J 25:821--855, 1976; Math Z 154:265--273, 1977) to an appropriate free boundary setting.

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Guofang Wang, Wei Wei, Chao Xia, Xuwen Zhang. 2026-09-11. Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary. https://arxiv.org/abs/2609.12630

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