Affiliation:
1. Departamento de Matemáticas , 16727 Universidad de Cádiz , Puerto Real , Spain
2. Department of Mathematics , Moulay Ismail University , Meknes , Morocco
Abstract
Abstract
In this paper, we analyze the following nonlinear elliptic problem
A
(
u
)
=
ρ
(
u
)
|
∇
φ
|
2
in
Ω
,
div
(
ρ
(
u
)
∇
φ
)
=
0
in
Ω
,
u
=
0
on
∂
Ω
,
φ
=
φ
0
on
∂
Ω
.
$\begin{cases}A\left(u\right)=\rho \left(u\right)\vert \nabla \varphi {\vert }^{2}\,\text{in}\,{\Omega},\quad \hfill \\ \text{div}\left(\rho \left(u\right)\nabla \varphi \right)=0\,\text{in}\,{\Omega},\quad \hfill \\ u=0\,\text{on}\,\partial {\Omega},\quad \hfill \\ \varphi ={\varphi }_{0}\,\text{on}\,\partial {\Omega}.\quad \hfill \end{cases}$
where A(u) = −div a(x, u, ∇u) is a Leray-Lions operator of order p. The second member of the first equation is only in L
1(Ω). We prove the existence of a bilateral solution by an approximation procedure, the keypoint being a penalization technique.
Funder
Ministerio de Ciencia e Innovación of the Spanish Government with the participation of the European Regional Development Fund (ERDF/FEDER).
Cited by
2 articles.
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