Superharmonicity of curvature function for the convex level sets of harmonic functions

We prove that the combination of the norm of gradient and the Gaussian curvature for the convex level sets of harmonic function is superharmonic.

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 60; no. 4
Main Authors Ma, Xi-Nan, Zhang, Wei
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Curvature
Harmonic functions
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
35B50
35B45
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Summary:We prove that the combination of the norm of gradient and the Gaussian curvature for the convex level sets of harmonic function is superharmonic.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02023-4