Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Guofang, Wei, Wei, Xia, Chao, Zhang, Xuwen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213133275