A Liouville theorem for the higher-order fractional Laplacian
2019 ◽
Vol 21
(02)
◽
pp. 1850005
◽
Keyword(s):
We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space [Formula: see text] by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on [Formula: see text] through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.
2021 ◽
Vol 60
(6)
◽
Keyword(s):
2013 ◽
Vol 65
(6)
◽
pp. 972-979
◽
2014 ◽
Vol 52
(3-4)
◽
pp. 641-659
◽
2007 ◽
Vol 126
(13)
◽
pp. 134112
◽
Keyword(s):
2015 ◽
pp. 157-169
Keyword(s):
2021 ◽
Vol 502
(1)
◽
pp. 125225