Nonlinear elliptic equations and Gauss measure

In this paper we study a Dirichlet problem relative to the equation Lu = g \phi - (f_i \phi)(x_i), where L is a non linear elliptic operator with a lower-order term whose ellipticity condition is given in terms of the function \phi(x), the density of the Gaussian measure. We use the notion of rearrangement with respect to the Gauss measure to obtain a priori estimate of the solution u and we study the summability of u in the Lorentz-Zygmund spaces when g and f_i vary in suitable Lorent-Zygmund spaces.