| Volume 4, Number 3, 2014, Pages 245-270 DOI：10.11948/2014012 |
| Entropy solutions to nonlinear elliptic anisotropic problem with variable exponent |
| Benboubker Mohamed Badr,Hjiaj Hassan,OUARO Stanislas |
| Keywords:Anisotropic Sobolev spaces |
| Abstract: |
| In this work, we give an existence result of entropy solutions for nonlinear anisotropic elliptic equation of the type $$- \mbox{div} \big( a(x,u,\nabla u)\big)+ g(x,u,\nabla u) + |u|^{p_{0}(x)-2}u = f-\mbox{div} \phi(u),\quad \mbox{ in } \Omega,$$ where $-\mbox{div}\big(a(x,u,\nabla u)\big)$ is a Leray-Lions operator, $\phi \in C^{0}(I\!\!R,I\!\!R^{N})$. The function $g(x,u,\nabla u)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, satisfying the sign condition and the datum $f$ belongs to $L^1(\Omega)$. |
PDF Download reader
|
|
|
|