On the moving plane method for singular solutions to semilinear elliptic equations

Abstract

We consider positive weak solutions to −Δu=f(x,u) in Ω∖Γ with u=0 on ∂Ω. We prove symmetry and monotonicity properties of the solutions in symmetric convex domains via the moving plane method, under suitable assumptions on f and on the singular set Γ. With similar arguments we also consider the case when the domain is the whole space and the nonlinearity has at most critical growth.