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Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector

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Abstract

In this paper we establish some symmetry results for positive solutions of semilinear elliptic equations with mixed boundary conditions. In particular, we show that the positive solution in a super-spherical sector must be symmetric. The monotonicity property is also proved. Our proof is based on the well-known moving plane methods.

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Acknowledgements

The authors sincerely thank the anonymous referee for careful reading and helpful suggestions which led to improvements of our original manuscript. The first author is supported by the Natural Science Foundation of China (Grant No. 12001543).

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Ruofei Yao

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Ruofei Yao

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Hongbin Chen

  4. Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX, 78249, USA

    Changfeng Gui

Authors
  1. Ruofei Yao
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  2. Hongbin Chen
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  3. Changfeng Gui
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Correspondence to Changfeng Gui.

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Communicated by O. Savin.

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Yao, R., Chen, H. & Gui, C. Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector. Calc. Var. 60, 130 (2021). https://doi.org/10.1007/s00526-021-01999-3

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