Local regularity results to nonlinear elliptic Dirichlet problems with lower order terms

In this paper we study local regularity properties of weak solutions to a class of nonlinear noncoercive elliptic Dirichlet problems with L1 datum. The model example is -Δp(w)+b(x)|Dw|p-1=f(x)inΩ,w=0on∂Ω.Here Ω ⊂ RN is a bounded open subset, N> 1 , - Δ p is the well known p-Laplace operator, 1 < p< N, b is a function in the Lorentz space LN,1(Ω) and f is a function in L1(Ω). We also investigate similar issues for a lower order perturbation of these problems