Symmetry of large solutions for semilinear elliptic equations in a symmetric convex domain

In this paper, we consider the solutions of the boundary blow-up problem {Delta u = 1/u(gamma) + f (u) in Omega, u > 0 in Omega, u = +infinity on partial derivative Omega, where gamma > 0, Omega is a bounded convex smooth domain and symmetric w.r.t. a direction. f is a locally Lipschitz continuous and non-decreasing function. We prove symmetry and monotonicity of solutions of the problem above by the moving planes method. A maximum principle in narrow domains plays an important role in proof of the main result.