Regularity results for degenerate elliptic equations related to Gauss measure

In this paper we study a Dirichlet problem relative to the equation Lu = g phi - (f(i)phi)(xi), where L is a linear elliptic operator with lower-order terms whose ellipticity condition is given in terms of the function phi (x) = (2 pi)(-n/2) exp (-|X|(2)/2), the density of the Gaussian measure. We use the notion of rearrangement with respect to the Gauss measure to obtain a priory estimate of the solution u and we study the summability of u in the Lorentz-Zygmund spaces when g and f(i) varies in suitable Lorent-Zygmund spaces.