Regularity and symmetry results for nonlinear degenerate elliptic equations

In this paper we prove regularity results for a class of nonlinear degenerateelliptic equations of the form $displaystyle -operatorname{div}(A(|ablau|)abla u)+Bleft( |abla u|ight) =f(u)$; in particular, we investigatethe second order regularity of the solutions. As a consequence of theseresults, we obtain symmetry and monotonicity properties of positive solutionsfor this class of degenerate problems in convex symmetric domains via asuitable adaption of the celebrated moving plane method of Alexandrov-Serrin.