A Half-Space Liouville Theorem for Anisotropic Minimal Graph with Free Boundary
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.
Authors
- Xuwen Zhang (ORCID: https://orcid.org/0000-0002-2281-6903)
- Wei Wu Wei
- Guofang Wang (ORCID: https://orcid.org/0000-0003-3456-6099)
- Chao Xia
Institutions
- University of Freiburg (DE)
- Xiamen University (CN)
- Nanjing University of Science and Technology (CN)
- Nanjing University (CN)
Publication Details
- Journal
- Archive for Rational Mechanics and Analysis
- Published
- 2026-05-18
- DOI
- https://doi.org/10.1007/s00205-026-02196-2
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Albert-Ludwigs-Universität Freiburg
- Natural Science Foundation of Fujian Province