Nonlinear elliptic equations with singular nonlinearities

In this paper we study nonlinear elliptic boundary value problems with singular nonlinearities whose simplest example is{div( |δu|p2δu ) = f u in ω, u =0 on ω, where ω is a bounded open set in R N (N ≥ 2),γ >0, 1 0 and how the regularity of u depends on the summability of f, on p and on γ. Keywords: nonlinear elliptic equations, singular elliptic equations, quasilinear elliptic equations with p-Laplacian. © 2013 - IOS Press and the authors. All rights reserved.