On the moving plane method for boundary blow-up solutions to semilinear elliptic equations

Abstract

Abstract We consider weak solutions to - Δ ⁢ u = f ⁢ ( u ) {-\Delta u=f(u)} on Ω 1 ∖ Ω 0 {\Omega_{1}\setminus\Omega_{0}} , with u = c ≥ 0 {u=c\geq 0} in ∂ ⁡ Ω 1 {\partial\Omega_{1}} and u = + ∞ {u=+\infty} on ∂ ⁡ Ω 0 {\partial\Omega_{0}} , and we prove monotonicity properties of the solutions via the moving plane method. We also prove the radial symmetry of the solutions in the case of annular domains.