Symmetry of odd solutions to equations with fractional Laplacian

被引：0

作者：

Djitte, Sidy M. ^{[1
,2
]}

Jarohs, Sven ^{[1
]}

机构：

[1] Goethe Univ Frankfurt AM, Inst Math, Robert Mayer Str 10, D-60325 Frankfurt, Germany

[2] African Inst Math Sci Senegal AIMS Senegal, KM 2,Route Joal,BP 14 18, Mbour, Senegal

来源：

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS | 2022年 / 8卷 / 01期

关键词：

Symmetries; Nonlocal operators; Sign-changing solutions; MOUNTAIN PASS SOLUTIONS;

D O I：

10.1007/s41808-022-00146-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has a fixed sign on one side, then it will be symmetric in the perpendicular direction. Moreover, the solution will be monotonic in the part where it is of fixed sign. In addition, we present also a class of examples in which our result can be applied.

引用

页码：209 / 230

页数：22

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