Antisymmetric maximum principles and Hopf’s lemmas for the Logarithmic Laplacian, with applications to symmetry results

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-01-27 DOI:10.1007/s10231-025-01549-0

Luigi Pollastro, Nicola Soave

引用次数: 0

Abstract

We prove antisymmetric maximum principles and Hopf-type lemmas for linear problems described by the Logarithmic Laplacian. As application, we prove the symmetry of solutions for semilinear problems in symmetric sets, and a rigidity result for the parallel surface problem for the Logarithmic Laplacian.

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对数拉普拉斯函数的反对称极大值原理和Hopf引理，及其在对称结果中的应用

我们证明了用对数拉普拉斯算子描述的线性问题的反对称极大原理和hopf型引理。作为应用，我们证明了对称集合中半线性问题解的对称性，并证明了对数拉普拉斯平行曲面问题的刚性结果。

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

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.