Abstract and Applied Analysis
Volume 2003 (2003), Issue 18, Pages 1005-1035
doi:10.1155/S1085337503306359

On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems

Davide Guidetti1 and Sergei Piskarev2

1Dipartimento di Matematica, Universitá di Bologna, Piazza di Porta S. Donato 5, Bologna 40126, Italy
2Science Research Computer Center, Moscow State University, Moscow 119899, Russia

Received 15 April 2003

Copyright © 2003 Davide Guidetti and Sergei Piskarev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give some results concerning the real-interpolation method and finite differences. Next, we apply them to estimate the resolvents of finite-difference discretizations of Dirichlet boundary value problems for elliptic equations in space dimensions one and two in analogs of spaces of continuous and Hölder continuous functions. Such results were employed to study finite-difference discretizations of parabolic equations.