Nonuniformly elliptic equations of p-Laplacian type

This paper deals with the existence of a generalized solution in W01,p(Ω) to a nonuniformly nonlinear elliptic equation of the form -div(a(x,∇u))=f(x,u) in a bounded domain Ω of Rn. Here a satisfies |a(x,ξ)|⩽c0[h0(x)+h1(x)|ξ|p-1] for any ξ in Rn, a.e. x∈Ω, h0∈Lpp-1(Ω), and h1∈Lloc1(Ω).