Comparison results for nonlinear degenerate Dirichlet and Neumann problems with general growth in the gradient

This paper deals with both Dirichlet and Neumann problems for a class of nonlinear degenerate elliptic equations with general growth in the gradient. First, we give an existence result of a spherically symmetric solution to the “symmetrized” problems with data depending only on the radials. Second, we prove that the solutions of the original problems can be compared, under a rearrangement, with the solutions of the “symmetrized” problems.