DIRECT METHOD OF MOVING PLANES FOR LOGARITHMIC LAPLACIAN SYSTEM IN BOUNDED DOMAINS

作者：Liu, Baiyu^*

来源：Discrete and Continuous Dynamical Systems, 2018, 38(10): 5339-5349.

DOI：10.3934/dcds.2018235

• Logarithmic Laplacian
• direct method of moving planes
• radial symmetry

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.

• 出版日期2018-10
• 单位北京科技大学