Affiliation:
1. Department of Mathematics , Laboratory LAMA Faculty of Sciences , Dhar-Mahrez, Fez , Morocco .
2. Sultan Moulay slimane University Laboratory LMACS , FST Beni-Mellal , Morocco .
3. Laboratory LSI , Polydisciplinary Faculty , Taza .
Abstract
Abstract
In this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form
-
∑
i
=
1
N
∂
i
a
i
(
x
,
u
,
∇
u
)
-
∑
i
=
1
N
∂
i
φ
i
(
u
)
=
f
,
$$ - \sum\limits_{i = 1}^N {{\partial _i}{a_i}(x,u,\nabla u) - } \sum\limits_{i = 1}^N {{\partial _i}{\phi _i}(u) = f,} $$
where the right hand side f belongs to L
1(Ω). The operator
-
∑
i
=
1
N
∂
i
a
i
(
x
,
u
,
∇
u
)
$- \sum\nolimits_{i = 1}^N {{\partial _i}{a_i}\left( {x,u,\nabla u} \right)} $
is a Leray-Lions anisotropic operator and ϕi
∈ C
0(ℝ,ℝ).
Subject
Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis
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