Regularity and symmetry results for nonlinear degenerate elliptic equations

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