Abstract and Applied Analysis
Volume 2003 (2003), Issue 18, Pages 1005-1035
On real interpolation, finite differences, and estimates
depending on a parameter for discretizations of elliptic
boundary value problems
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.
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.