Integrability for solutions to some anisotropic elliptic equations
We consider the boundary value problem { ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = 0 , x ∈ Ω ; u ( x ) = u ∗ ( x ) , x ∈ ∂ Ω . We show that, higher integrability of the boundary datum u ∗ forces solutions u to have higher integrability as well. Assumptions on a i ( x , z ) are suggested by the Euler...
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| Veröffentlicht in: | Nonlinear analysis 2012-03, Vol.75 (5), p.2867-2873 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We consider the boundary value problem
{
∑
i
=
1
n
D
i
(
a
i
(
x
,
D
u
(
x
)
)
)
=
0
,
x
∈
Ω
;
u
(
x
)
=
u
∗
(
x
)
,
x
∈
∂
Ω
.
We show that, higher integrability of the boundary datum
u
∗
forces solutions
u
to have higher integrability as well. Assumptions on
a
i
(
x
,
z
)
are suggested by the Euler equation of the anisotropic functional
∫
Ω
(
|
D
1
u
|
p
1
+
|
D
2
u
|
p
2
+
⋯
+
|
D
n
u
|
p
n
)
d
x
. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2011.11.028 |