Nonuniformly elliptic equations of p-Laplacian type Original Research Article

This paper deals with the existence of a generalized solution in View the MathML sourceW01,p(Ω) to a nonuniformly nonlinear elliptic equation of the form -div(a(x,∇u))=f(x,u)-div(a(x,∇u))=f(x,u) in a bounded domain ΩΩ of RnRn. Here a satisfies |a(x,ξ)|⩽c0[h0(x)+h1(x)|ξ|p-1]|a(x,ξ)|⩽c0[h0(x)+h1(x)|ξ|p-1] for any ξξ in RnRn, a.e. x∈Ωx∈Ω, View the MathML sourceh0∈Lpp-1(Ω), and View the MathML sourceh1∈Lloc1(Ω).