What question did this study set out to answer?

Investigate the Serrin-type overdetermined boundary value problem for the anisotropic Finsler infinity Laplacian on bounded, convex domains.

August 20, 2026Communications in Partial Differential Equations

The overdetermined problem for an anisotropic infinity Laplacian

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Authors

FLFang LiuNanjing University of Science and Technology YWYuting WangNanjing University of Science and Technology XYXiaoping YangNanjing University

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Implication

Theoretical analysis reveals that overdetermined Finsler infinity Laplacian solutions exist only on anisotropic stadium-like domains, extending geometric rigidity results to directional norms.

Key Points

Investigate the Serrin-type overdetermined boundary value problem for the anisotropic Finsler infinity Laplacian on bounded, convex domains.
Introduced and formulated anisotropic gradient flow for directional Finsler norms.
Combined the convex envelope method with Weinberger's technique to evaluate the existence of $C^1$-viscosity solutions.
Proved that the existence of a $C^1$-viscosity solution to the overdetermined problem strictly characterizes anisotropic stadium-like domains.
Generalized previous isotropic rigidity results established by Crasta and Fragalà to general anisotropic Finsler geometries.

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/6a86b6208a91293e6a1cdccd https://doi.org/10.1080/03605302.2026.2714975

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Implication

Theoretical analysis reveals that overdetermined Finsler infinity Laplacian solutions exist only on anisotropic stadium-like domains, extending geometric rigidity results to directional norms.