The Hardy inequality and nonlinear parabolic equations on Carnot groups
In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation: { ∂ u ∂ t = Δ G , p u + V ( x ) u p − 1 in Ω × ( 0 , T ) , 1 < p < 2 , u ( x , 0 ) = u 0 ( x ) ≥ 0 in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , where Δ...
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| Veröffentlicht in: | Nonlinear analysis 2008-12, Vol.69 (12), p.4643-4653 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:
{
∂
u
∂
t
=
Δ
G
,
p
u
+
V
(
x
)
u
p
−
1
in
Ω
×
(
0
,
T
)
,
1
<
p
<
2
,
u
(
x
,
0
)
=
u
0
(
x
)
≥
0
in
Ω
,
u
(
x
,
t
)
=
0
on
∂
Ω
×
(
0
,
T
)
,
where
Δ
G
,
p
is the
p
-sub-Laplacian on a Carnot group
G
and
V
∈
L
loc
1
(
Ω
)
. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2007.11.020 |