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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 ℝ3+ 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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Cite

BibTeXRIS
BibTeX
@misc{wang2026bernstein,
  title = {{Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary}},
  author = {Guofang Wang and Wei Wei and Chao Xia and Xuwen Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12630},
  eprint = {2609.12630},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12630},
}
RIS
TY  - UNPB
TI  - Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary
AU  - Guofang Wang
AU  - Wei Wei
AU  - Chao Xia
AU  - Xuwen Zhang
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12630
UR  - https://arxiv.org/abs/2609.12630
AB  - 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 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.
ER  -