Existence results for a class of degenerate elliptic equations

Abstract

In the present paper we prove existence results for a class of nonlinear elliptic equations whose prototype is -div (|D u|^(p−2) Du ϕ( x) ) + |D u|^σ ϕ( x)= g ϕ ; where Ω is an open set, u=0 on \partial Ω; the function ϕ( x) = (2π)^ (n/2) exp (−|x|2 /2) is the density of Gauss measure and g \in the weighted Lorentz-Zygmund space L^r (log L)^(-1/2) (ϕ,Ω), 1<r<p’. The results are sharp in this class of spaces