A direct method of moving planes for the Logarithmic Laplacian

A direct method of moving planes for the Logarithmic Laplacian

In this paper, a direct method of moving planes for the Logarithmic Laplacian is developed. Some key concepts of the method such as Maximum principle for anti-symmetric functions, Narrow region principle and Decay at infinity are discussed. As an application of the direct method of moving planes, th...

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Veröffentlicht in:Applied mathematics letters 2021-08, Vol.118, p.107141, Article 107141
Hauptverfasser: Zhang, Lihong, Nie, Xiaofeng
Format: Artikel
Sprache:eng
Schlagworte:
Logarithmic Laplacian
Symmetry and monotonicity
The direct method of moving planes
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Zusammenfassung:In this paper, a direct method of moving planes for the Logarithmic Laplacian is developed. Some key concepts of the method such as Maximum principle for anti-symmetric functions, Narrow region principle and Decay at infinity are discussed. As an application of the direct method of moving planes, the symmetry and monotonicity of the positive solutions of two nonlinear equations involving Logarithmic Laplacian are obtained.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2021.107141