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An application of a theorem of G. Zwirner to a class of non-linear elliptic systems in divergence form
A theorem on the solutions of the problem U ′ ( w ) = γ F ( U ( w ) , w ) , U ( w 1 ) = u 1 , U ( w 2 ) = u 2 is applied for finding the functional solutions of the system of partial differential equations ∇ · ( a ( u , w ) ∇ u ) = 0 , u = u 1 on Γ 1 , u = u 2 on Γ 2 , ∂ u ∂ n = 0 on Γ 3 ∇ · ( b ( u...
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| Published in: | Bollettino della Unione matematica italiana (2008) 2018-12, Vol.11 (4), p.533-539 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | A theorem on the solutions of the problem
U
′
(
w
)
=
γ
F
(
U
(
w
)
,
w
)
,
U
(
w
1
)
=
u
1
,
U
(
w
2
)
=
u
2
is applied for finding the functional solutions of the system of partial differential equations
∇
·
(
a
(
u
,
w
)
∇
u
)
=
0
,
u
=
u
1
on
Γ
1
,
u
=
u
2
on
Γ
2
,
∂
u
∂
n
=
0
on
Γ
3
∇
·
(
b
(
u
,
w
)
∇
w
)
=
0
,
w
=
w
1
on
Γ
1
,
w
=
w
2
on
Γ
2
,
∂
w
∂
n
=
0
on
Γ
3
.
The problem of existence and uniqueness of solutions is considered. |
|---|---|
| ISSN: | 1972-6724 2198-2759 |
| DOI: | 10.1007/s40574-017-0150-0 |