An elliptic equation with power nonlinearity and degenerate coercivity

We discuss the existence and regularity of solutions to the following Dirichlet problem: $$\begin{array}{cccc}& {\displaystyle \{\begin{array}{ll}-\text{div}\left(\frac{Du}{(1+\mathrm{\mid }u\mathrm{\mid }{)}^{\theta }}\right)=-\text{div}(u^{\gamma }E(x))+f(x)& in\mathrm{\Omega },\\ u(x)=0& on\mathrm{\partial }\mathrm{\Omega },\end{array}}& & \end{array}$$ where $\theta ,\gamma >0$. An interesting feature of this problem is the interplay between the two nonlinearities, the degeneracy and the power nonlinearity.