Affiliation:
1. Department of Mathematics , University of Algiers , Algiers, Algeria. 2 Street Didouche Mourad Algiers. Laboratory LEDPNL,HM, ENS-Kouba, Algiers , Algeria .
Abstract
Abstract
We study the existence and regularity results for non-linear elliptic equation with degenerate coercivity and a singular gradient lower order term. The model problems is
{
-
d
i
v
(
b
(
x
)
|
∇
u
|
p
-
2
∇
u
(
1
+
|
u
|
)
γ
)
+
|
∇
u
|
p
|
u
|
θ
=
f
,
i
n
Ω
,
u
=
0
,
o
n
∂
Ω
,
\left\{ {\matrix{ { - div\left( {b\left( x \right){{{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \over {\left( {1 + \left| u \right|} \right)\gamma }}} \right) + {{{{\left| {\nabla u} \right|}^p}} \over {{{\left| u \right|}^\theta }}} = f,} \hfill & {in\,\Omega ,} \hfill \cr {u = 0,} \hfill & {on\,\partial \Omega ,} \hfill \cr } } \right.
swhere Ω is a bounded open subset in ℝN, 1 ≤ θ < 2, p > 2 and γ > 0. We will show that, even if the lower order term is singular, we obtain existence and regularity of positive solution, under various assumptions on the summability of the source f.
Subject
Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis
Cited by
5 articles.
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