Discrete Green's functions

Authors:
G. T. McAllister and E. F. Sabotka

Journal:
Math. Comp. **27** (1973), 59-80

MSC:
Primary 65P05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0341909-9

MathSciNet review:
0341909

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the discrete Green's function over a discrete *h*-convex region of the plane; i.e., for for . Assume that and are Hölder continuous over and positive. We show that and , where is an *m*th order difference quotient with respect to the components of *P* or *Q*, and denotes an *m*th order difference quotient only with respect to the components of *P*.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0341909-9

Keywords:
Elliptic difference equations,
finite differences

Article copyright:
© Copyright 1973
American Mathematical Society