Nonlinear Singular Elliptic Equations of p-Laplace Type with Superlinear Growth in the Gradient.

We consider a singular nonlinear elliptic Dirichlet problems with lower-order terms, where the combined effects of a superlinear growth in the gradient and a singular term allow us to establish some existence and regularity results. The model problem is 0.1 - div (| ∇ u | p - 2 ∇ u) + μ | u | p - 1 u = b (x) | ∇ u | q u θ + f (x) u γ in Ω , u = 0 on ∂ Ω , where Ω is an open and bounded subset of R N , μ ≥ 0 , 0 < θ ≤ 1 , 0 ≤ γ < 1 and f is a nonnegative function that belong to some Lebesgue space. [ABSTRACT FROM AUTHOR]