Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-05-03 DOI:10.1007/s13540-024-00285-1

Lihong Zhang, Xiaofeng Nie

引用次数: 0

Abstract

In this paper, we prove Hopf’s lemma for the Logarithmic Laplacian. At first, we introduce the strong minimum principle. Then Hopf’s lemma for the Logarithmic Laplacian in the ball is proved. On this basis, Hopf’s lemma of the Logarithmic Laplacian is extended to any open set with the property of the interior ball. Finally, an example is given to explain Hopf’s lemma can be applied to the study of the symmetry of the positive solution of the nonlinear Logarithmic Laplacian problem by the moving plane method.

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对数拉普拉奇问题的霍普夫定理和径向对称性

在本文中，我们证明了对数拉普拉卡矩的 Hopf Lemma。首先，我们介绍强最小原理。然后证明了球中对数拉普拉斯的霍普夫两难。在此基础上，将对数拉普拉奇的霍普夫 Lemma 推广到任何具有内球性质的开集。最后，举例说明了霍普夫两难可以应用于用移动平面法研究非线性对数拉普拉斯问题正解的对称性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.