The Dirichlet problem for the non-linear elliptic partial differential equationna(x,y,u(x,y))u,xx + e(x,y,u(x,y))u, - 7(x,y,u(x,y))u - 0nis studied. It is assumed that the coefficients are strictly positive and Lipschitz in the argument u(x,y). It is then proved that the solution may be uniformly approximated by the solution to the associated difference equation provided that a certain inequality, relating bounds on the coefficients, is satisfied.
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