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Liouville type theorems for positive harmonic functions on the unit ball with a nonlinear boundary condition

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Abstract

We obtain some Liouville type theorems for positive harmonic functions on the unit ball with a nonlinear boundary condition. The proof is based on an integral identity and some Sobolev inequalities on the sphere.

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Acknowledgements

The authors would like to thank Prof. Xi-Nan Ma for his discussions and advice. Research of the first author was supported by NSFC 12141105 and YF 0010450004. Research of the second author was supported by NSFC 11861016 and NSFC 12141105.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230006, Anhui Province, People’s Republic of China

    Daowen Lin

  2. School of Mathematics and Statistics, GuangXi Normal University, Guilin, 541004, Guangxi Province, People’s Republic of China

    Qianzhong Ou

Authors
  1. Daowen Lin
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  2. Qianzhong Ou
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Correspondence to Daowen Lin.

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Communicated by L. Szekelyhidi.

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Lin, D., Ou, Q. Liouville type theorems for positive harmonic functions on the unit ball with a nonlinear boundary condition. Calc. Var. 62, 34 (2023). https://doi.org/10.1007/s00526-022-02376-4

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