What question did this study set out to answer?

The research aims to establish a Liouville-type theorem for anisotropic minimal graphs with free boundaries in a half-space.

May 19, 2026Archive for Rational Mechanics and Analysis0 citationsOpen Access

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

GWGuofang WangUniversity of Freiburg WWWei Wu WeiNanjing University of Science and Technology CXChao XiaXiamen University

Key Points

The research aims to establish a Liouville-type theorem for anisotropic minimal graphs with free boundaries in a half-space.
Proved the theorem for anisotropic minimal graphs in a half-space with one-sided linear growth.
Built on classical results by Bombieri–De Giorgi–Miranda and Simon.
Considered conditions emphasizing the free boundary setting.
Demonstrated that any anisotropic minimal graph with specified growth conditions is flat in the half-space setting.
Extended classical results to relate to free boundary scenarios.

Abstract

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.

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Cite This Study

Wang et al. (Mon,) studied this question.

synapsesocial.com/papers/6a0bfe08166b51b53d3794fc https://doi.org/https://doi.org/10.1007/s00205-026-02196-2

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