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

Abstract

We consider weak solutions to -Δ⁢u=f⁢(u){-\Delta u=f(u)} on Ω1∖Ω0{\Omega_{1}\setminus\Omega_{0}}, with u=c≥0{u=c\geq 0} in ∂⁡Ω1{\partial\Omega_{1}} and u=+∞{u=+\infty} on ∂⁡Ω0{\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.

Keywords

• elliptic equations
• boundary blow-up
• symmetry of solutions
• radial symmetry,moving plane method
• 35b01
• 35j61
• 35j75