Affiliation:
1. Department of Mathematics , State University of Londrina , Londrina - PR - Brazil , 86057-970.
Abstract
Abstract
In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations
{
-
div
[
𝒜
(
x
,
∇
u
)
ω
1
+
(
x
,
u
,
∇
u
)
ω
2
]
=
f
0
(
x
)
-
∑
j
=
1
n
D
j
f
j
(
x
)
in
Ω
,
u
(
x
)
=
0
on
∂
Ω
,
\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.
in the setting of the weighted Sobolev spaces.
Subject
Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis
Reference20 articles.
1. [1] D. Bresch, J. Lemoine, F. Guíllen-Gonzalez, A note on a degenerate elliptic equation with applications for lake and seas, Electron. J. Differential Equations, vol. 2004 (2004), No. 42, 1-13.
2. [2] A.C.Cavalheiro, Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems, J. Appl. Anal., 19 (2013), 41-54.10.1515/jaa-2013-0003
3. [3] A.C.Cavalheiro, Existence results for Dirichlet problems with degenerate p-Laplacian, Opuscula Math., 33, no 3 (2013), 439-453.
4. [4] A.C.Cavalheiro, Topics on Degenerate Elliptic Equations, Lambert Academic Publishing, Germany (2018).
5. [5] M. Chipot, Elliptic Equations: An Introductory Course, Birkhäuser, Berlin (2009).
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