On the Neumann Problem for some Linear and Non-linear Uniformly Elliptic Difference Equations

In this paper we obtain a priori bounds on difference quotientsto the solution of the second boundary value problem for somelinear uniformly elliptic difference equations over rectangularregions. These results are applied to the constructive solutionof mildly non-linear and mildly quasi-linear uniformly ellipticdifference equations.     

Mixed Boundary Value Problems for some Linear and Non-linear Elliptic Difference Equations

We obtain a priori bounds on difference quotients for some mixedboundary value problems associated with uniformly elliptic differenceequations over rectangular regions. These results are appliedto mildly quasi-linear and mildly non-linear problems to establishexistence and uniqueness criteria. Our estimates are usefulin the numerical computation of these solutions.