Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient

In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a Leray-Lions operator defined on W (Ω), and H(x, u, Du) grows with respect to Du at most like |Du| , p-1 ≤ q ≤ p. Comparison results are obtained between the rearrangement of a solution u of Dirichlet problem quoted above and the rearrangement of the solution of a problem whose data are radially symmetric.