Work

A Half-Space Liouville Theorem for Anisotropic Minimal Graph with Free Boundary

Year: 2026

Type: article

Abstract: In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-sided linear growth. This extends the classical results of Bombieri–De Giorgi–Miranda (Arch Rational Mech Anal 32:255–267, 1969) and Simon (Indiana Univ Math J 25:821–855, 1976) to an appropriate free boundary setting.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02196-2

Authors: Guofang Wang, Wei Wei, Chao Xia, Xuwen Zhang

Institutions: University of Freiburg, Nanjing University, Xiamen University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Natural Science Foundation of China, Albert-Ludwigs-Universität Freiburg, Natural Science Foundation of Fujian Province