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

Baiyu Liu

doi:10.3934/dcds.2018235

Article Contents

2018, Volume 38, Issue 10: 5339-5349. Doi: 10.3934/dcds.2018235

This issue Previous Article Stability analysis for a family of degenerate semilinear parabolic problems Next Article

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

Baiyu Liu^,

School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District Beijing 100083, China

* Corresponding author: Baiyu Liu
* Corresponding author: Baiyu Liu

Received: April 30, 2018

Revised: April 30, 2018

Published: September 2018

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.

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

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