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Direct method of moving planes for logarithmic Laplacian system in bounded domains

  • * Corresponding author: Baiyu Liu

    * Corresponding author: Baiyu Liu
The author is supported by the National Natural Science Foundation of China (No.11671031) and the Fundamental Research Funds for the Central Universities FRF-BR-17-013A.
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  • Chen, Li and Li [Adv. Math., 308(2017), pp. 404-437] developed a direct method of moving planes for the fractional Laplacian. In this paper, we extend their method to the logarithmic Laplacian. We consider both the logarithmic equation and the system. To carry out the method, we establish two kinds of narrow region principle for the equation and the system separately. Then using these narrow region principles, we give the radial symmetry results for the solutions to semi-linear logarithmic Laplacian equations and systems on the ball.

    Mathematics Subject Classification: Primary: 35R11; Secondary: 35B50.


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