Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems
We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is: - div ( M ( x ) ∇ u ) + g ( u ) | ∇ u | 2 = - div ( E ( x , u ) ) + f ( x ) in Ω , u = 0 on ∂ Ω , where Ω is an open bounded subset of R N and f ∈ L 1 ( Ω ) . Despite this poor summability...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022-07, Vol.116 (3), Article 95 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is:
-
div
(
M
(
x
)
∇
u
)
+
g
(
u
)
|
∇
u
|
2
=
-
div
(
E
(
x
,
u
)
)
+
f
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is an open bounded subset of
R
N
and
f
∈
L
1
(
Ω
)
. Despite this poor summability, we prove the existence of finite energy solutions due to the effect of the presence of the term
g
(
u
)
|
∇
u
|
2
. |
|---|---|
| ISSN: | 1578-7303 1579-1505 |
| DOI: | 10.1007/s13398-022-01232-6 |