TY  - JOUR
ID  - Cavalheiro2014
LB  - Cavalheiro2014
AU  - Cavalheiro, Albo Carlos
TI  - Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations
ST  - Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 1
SP  - 15
EP  - 28
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.1.15
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.1.15
AB  - In this paper we are interested in the existence of solutions for the Dirichlet problem associated with degenerate nonlinear elliptic equations \[\begin{split}&-\sum_{j=1}^n D_j{\bigl[}{\omega}(x) {\cal A}_j(x, u, {\nabla}u){\bigr]} + b(x, u, {\nabla}u)\,{\omega}(x) + g(x)\,u(x)=\\&= f_0(x) - \sum_{j=1}^nD_jf_j(x) \quad{\rm on}\quad {\Omega}\end{split}\] in the setting of the weighted Sobolev spaces \({\rm W}_0^{1,p}(\Omega, \omega)\).
KW  - degenerate nonlinear elliptic equations
KW  - weighted Sobolev spaces
SN  - 1232-9274
ER  -