Mesh-independent a priori bounds for nonlinear elliptic finite difference boundary value problems

P. J. McKenna, W. Reichel, A. Verbitsky

In this paper we prove mesh independent a priori $L^{\infty }$-bounds for positive solutions of the finite difference boundary value problem $$ -Δ_h u = f(x,u) \mbox{ in } Ω_h, \quad…