Symmetry of solutions of some semilinear elliptic equations with singular nonlinearities

摘要

We consider positive solutions to the singular semilinear elliptic equation -δu=1uγ+f(u), in bounded smooth domains, with zero Dirichlet boundary conditions.We provide some weak and strong maximum principles for the H01(Ω) part of the solution (the solution u generally does not belong to H01(Ω)), that allow to deduce symmetry and monotonicity properties of solutions, via the Moving Plane Method.