Abstract
Abstract
In the paper, we study the global higher regularity and decay estimates of the positive solutions for the following fractional equations
{
(
−
Δ
)
s
u
+
u
=
|
u
|
p
−
2
u
in
R
N
,
lim
|
x
|
→
∞
u
(
x
)
=
0
,
u
∈
H
s
(
R
N
)
,
(0.1)
where
s
∈
(
0
,
1
)
,
N
>
2
s
,
2
<
p
<
2
s
∗
:=
2
N
N
−
2
s
and
(
−
Δ
)
s
is the fractional Laplacian. Let Q be a positive solution of (0.1). We prove that
Q
∈
C
k
,
γ
(
R
N
)
∩
H
k
(
R
N
)
and obtain the decay estimates of D
k
Q as
|
x
|
→
∞
for all
k
∈
N
+
and
γ
∈
(
0
,
1
)
. The argument relies on the Bessel kernel, comparison principle, Fourier analysis and iteration methods.
Funder
National R&D Program of China
National Natural Science Foundation of China