TY - JOUR
T1 - Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups
AU - Kassymov, Aidyn
AU - Ruzhansky, Michael
AU - Suragan, Durvudkhan
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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.
AB - 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.
KW - Blow-up
KW - Fractional logarithmic Caffarelli–Kohn–Nirenberg inequality
KW - Fractional logarithmic Gagliardo–Nirenberg inequality
KW - Fractional logarithmic Sobolev inequality
KW - Homogeneous group
UR - http://www.scopus.com/inward/record.url?scp=85076893668&partnerID=8YFLogxK
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U2 - 10.1007/s00030-019-0610-6
DO - 10.1007/s00030-019-0610-6
M3 - Article
AN - SCOPUS:85076893668
SN - 1021-9722
VL - 27
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 1
M1 - 7
ER -