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A priori bounds on difference quotients of solutions to some linear uniformly elliptic difference equations

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Abstract

Second order difference quotients of solutions to a class of linear uniformly elliptic difference Dirichlet problems are bounded in terms of quantities which depend on the coefficients of the operator, the inhomogenous term, the boundary values and the domain-which we take to be a rectangle. The results we obtain have theoretical and practical applications.

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  1. Center for the Application of Mathematics, Lehigh University, 203 E. Packer Avenue, 18015, Bethlehem, Pennsylvania, USA

    G. T. McAllister

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  1. G. T. McAllister
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McAllister, G.T. A priori bounds on difference quotients of solutions to some linear uniformly elliptic difference equations. Numer. Math. 11, 13–37 (1968). https://doi.org/10.1007/BF02165468

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