Existence results for nonlinear elliptic equations related to Gauss measure in a limit case

The aim of this paper is to prove existence results for nonlinear elliptic equations whose the prototype is −div (|u|^(p−2)u )= g ϕ in a open subset Ω of R^n, , u = 0 on \partial Omega , where p ≥2, the function ϕ( x) = (2π)^ (n/2) exp (−|x|^2 /2) is the density of Gauss measure and g \in L^1 (log L)^(1/2) This condition on the function g is sharp in the class of Zygmund spaces