Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

被引：0
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作者：
Aidyn Kassymov
Michael Ruzhansky
Durvudkhan Suragan
机构：
[1] Al-Farabi Kazakh National University,Department of Mathematics: Analysis, Logic and Discrete Mathematics
[2] Ghent University,School of Mathematical Sciences
[3] Institute of Mathematics and Mathematical Modeling,Department of Mathematics
[4] Queen Mary University of London,undefined
[5] Nazarbayev University,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2020年 / 27卷
关键词：
Fractional logarithmic Sobolev inequality; Fractional logarithmic Gagliardo–Nirenberg inequality; Fractional logarithmic Caffarelli–Kohn–Nirenberg inequality; Blow-up; Homogeneous group; 22E30; 43A80;
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摘要：
In this paper, we prove the fractional logarithmic Sobolev inequality on homogeneous groups. Also, we establish fractional logarithmic Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups. In addition, we show blow-up results for the fractional heat equation with logarithmic nonlinearity on homogeneous groups.
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