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.

中文翻译：

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对数拉普拉斯问题的 Hopf 引理和径向对称性

在本文中，我们证明了对数拉普拉斯算子的霍普夫引理。首先，我们介绍强最小原则。然后证明了球中对数拉普拉斯算子的Hopf引理。在此基础上，Hopf的对数拉普拉斯引理被推广到任何具有内球性质的开集。最后举例说明Hopf引理可以应用于用动平面法研究非线性对数拉普拉斯问题正解的对称性。