Some adaptations of the moving planes method to singular elliptic problems

In this talk we will consider positive singular solutions to some quasilinear elliptic problems under zero Dirichlet boundary conditions. We will study qualitative properties of the solutions via the moving plane procedure, that goes back to the celebrated papers of Alexandrov and Serrin. In particular, exploiting a fine adaptation of the moving plane procedure and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions in bounded smooth domains.